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Full text of "Transactions of the Royal Society of Edinburgh"

«SH 




SA.C14-I 



'15M;.R1902 



TRANSACTIONS 



OF THE 



ROYAL SOCIETY OF EDINBURGH. 



VOL. XL. PART I.— FOR THE SESSION 1900-1. 



CONTENTS. 

I. A Contribution to the Life-Histories of the God and Whiting. By Arthur T. Masterman, 
M.A., D.Sc. (Lond. and St. And.), F.R.S.E. (With Three Plates), . 
(Issued separately, 6th July 1900.) 

II. Two Historical Fallacies : Heather Beer and Uisge Beithe. By Robert C. Maclagan, 
F.R.S.E., .......... 

(Issued separately, 23rd August 1900.) 

III. On the Eliminant of a Set of General Ternary Quadrics. (Part II.) By Thomas Muir, 

LL.D., 

(Issued separately, 23rd August 1900.) 

IV. On the Convection of Heat by Air Currents. By Prof. A. Crichton Mitchell. (With 
a Plate), .......... 

(Issued separately 10th November 1900.) 

V. A Development of a Pfajfian having a Vacant Minor. By Thomas Muir, LL.D., 

(Issued separately 15th November 1900.) 

VI. Contributions to the Cranioloyy of the People of the Empire of India. Part II. The 
Aborigines of ChMa NdgpUr and of the Central Provinces, the People of Orissa, the 
Veddalis and Negritos. By Prof. Sir Wm. Turner, K.C.B., D.C.L., F.R.S. (With 
Four Plates), ......... 

(Issued separately, 8th March 1901.) 

VII. Notes on the Dynamics of Cyclones and Anticyclones. By John Aitken, F.R.S. (With 
a Plate), .......... 

(Issued separately, 6th April 1901.) 

VIII. Observations of the Edinburgh Rock Thermometers. By Thomas Heath, B.A., Assistant 
Astronomer, Royal Observatory, Edinburgh. (With Four Plates), . 
(Issued separately 19th June 1901.) 

IX. Some Identities connected with Alternants, and with Elliptic Functions. By Thomas 
Muir, LL.D., . . . 

(Issued separately llflh June 1901.) 

X. The Hessian of a General Determinant. By Thomas Muik, LL.D., 

(Issued separately 4th June 1901.) 

XL The Differentiation of a Continuant. By Thomas Muir, LL.D., . 

(Issued separately 26th June 1901.) 



Page 



15 



23 



39 



49 



51) 



131 



157 



187 



203 



209 




EDINBURGH: 

PUBLISHED BY ROBERT GRANT & SON, 107 PRINCES STREET, 
AND WILLIAMS & NORGATE, 14 HENRIETTA STREET, COVENT GARDEN, LONDON. 



MDCCCCI. 

Price Twenty-five Shillings. 



y 



TEANSACTIONS 



OF THE 



ROYAL SOCIETY OF EDINBURGH 



TRANSACTIONS 



OF THE 



ROYAL SOCIETY 



OF 



EDINBURGH 



VOL. XL. 




EDINBURGH: 

PUBLISHED BY ROBEKT GRANT & SON, 107 PRTNCES STREET. 
AND WILLIAMS & NORGATE, 14 HENRIETTA STREET, COVENT GARDEN, LONDON. 



MDCCCCV. 



No. 



I. 


Published 


July 6, 1900. 


No. 


XVIII. 


Published 


April 24, 1902. 


II. 


)> 


August 23, 1900. 


» 


XIX. 


» 


May 27, 1902. 


III. 


>> 


August 23, 1900. 


>> 


XX. 


M 


June 16, 1902. 


IV. 


j) 


November 10, 1900. 


>) 


XXI. 


}> 


September 5, 1902. 


V. 


?> 


November 15, 1900. 


>) 


XXII. 


>) 


September 26, 1902 


VI. 


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March 8, 1901. 


»> 


XXIII. 


)) 


December 31, 1902. 


VII. 


>) 


April 6, 1901. 


ii 


XXIV. 


)) 


February 10, 1903. 


VIII. 


)> 


June 19, 1901. 


)> 


XXV. 


)> 


March 6, 1903. 


IX. 


)j 


June 14, 1901. 


j> 


XXVI. 


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April 21, 1903. 


X. 


>» 


June 4, 1901. 


j) 


XXVII. 


>> 


September 12, 1903 


XI. 


n 


June 26, 1901. 


j> 


XXVIII. 


)> 


October 16, 1903. 


XII. 


?) 


August 26, 1901. 


j> 


XXIX. 


J> 


October 30, 1903. 


XIII. 


)> 


October 26, 1901. 


»> 


XXX. 


)) 


October 31, 1903. 


XIV. 


)> 


November 12, 1901. 


>> 


XXXI. 


>) 


December 6, 1903. 


XV. 


>> 


December 16, 1901. 


>) 


XXXII. 


)) 


December 31, 1903. 


XVI. 


>) 


February 25, 1902. 


)> 


XXXIII. 


)) 


January 26, 1905. 


XVII. 


>> 


April 7, 1902. 











CONTENTS. 



PAET I. (1900-01.) 

NUMBER PAGE 

I. A Contribution to the Life- Histories of the Cod and Whiting. By 
Arthur T. Masterman, M.A., D.Sc. (Loncl. and St And.), F.R.S.E. 
(With Three Plates), ....... 1 

II. Two Historical Fallacies : Heather Beer and Uisge Beithe. By Robert 

C. Maclaoan, F.R.S.E., . . . . . .15 

III. On the Eliminant of a Set of General 'Ternary Qua dries. (Part II.) 

By Thomas Mtjir, LL.D., . . . . . .23 

IV. On the Convection of Heat by Air Currents. By Professor A. Crichton 

Mitchell. (With a Plate), ...... 39 

V. A Development of a Pfoffian having a Vacant Minor. By Thomas 

Muir, LL.D., ........ 49 

VI. Contributions to the Craniology of the People of the Empire of India. 
(Part II.) The Aborigines of Chuta Ndgptir and of the Central 
Provinces, the People of Orissa, the Veddahs and Negritos. By 
Professor Sir Wm. Turner, K.C.B., D.C.L., F.R.S. (With Four 
Plates), ........ 59 

VII. Notes on the Dynamics of Cyclones and Anticyclones. By John Aitken, 

F.R.S. (With a Plate), . . . . . .131 

VIII. Observations of the Edinburgh Rock Thermometers. By Thomas Heath, 
B.A., Assistant Astronomer, Royal Observatory, Edinburgh. (With 
Four Plates), ....... 



IX. Some Identities connected with Alternants, and, with Elliptic Functions 
By Thomas Muir, LL.D., . 

X. The Hessian of a General Determinant. By Thomas Muir, LL.D., 

XL The Differentiation of a Continuant. By Thomas Muir, LL.D., 



157 

187 
203 
209 



yi CONTENTS. 

PART II. (1901-02.) 

NUMBER PAGE 

XII. Ice- Erosion in the Cuillin Hills, Skye. By Alfred Harker, M.A., 

F.G.S. (With a Map), ...... 221 

XIII. The General Form of the Involutive 1 — 1 QuaAric Transformation in 

a Plane. By Charles Tweedie, M.A., B.Sc., . . . 253 

XIV. Apparatus for Measuring Strain and Applying Stress : with an 

Account of some Experiments on the Behaviour of Iron and Steel 
under Stress. By E. G. Coker, D.Sc. (With Eight Plates), . 263 

XV. On the Anatomy of a Collection of Slugs from N. W. Borneo ; with a 
List of Species recorded from that Region. By Walter E. Collinge, 
Lecturer on Zoology and Comparative Anatomy in the University of 
Birmingham. (With Three Plates), . . . . .295 

XVI. The True Shape, Relations, and, Structure of the Alimentary Viscera 
of the Porpoise (Phocoena communis), as displayed by the Formal 
Method. By David Hepburn, M.D., F.R.S.E., and David Water- 
ston,M.A., M.D., F.R.S.E. (With Three Plates), . . .313 

XVII. On the Primary Structure of certain Palceozoic Stems with the 
Dadoxylon Type of Wood. By D. H. Scott, M.A., Ph.D., F.R.S. 
(With Six Plates), . . . . . .331 

XVIII. On a Possible Stridulating Organ in the Mosquito. (Anopheles 
maculipennis, Meig.) By A. E. Shipley, M.A., and Edwin Wilson, 
F.E.S. (With a Plate), . . . . . .367 

XIX. The Early Derdopnv nt of Cnbrella oculata (Forbes), with Remarks on 
Echinoderm Development. By Arthur T. Masterman, M.A., D.Sc, 
F.RS.E. (With Five Plates), . . . . .373 

XX. A Bathymetrical and Geological Study of the Lakes of Snowdonia and 
Eastern Carnarvonshire. By T. J. Jehu, M.B., B.Sc. (Edin.), M.A. 
(Camb.), F.G.S. (With Eight Plates), . . . .419 



PART III. (1902-03.) 

XXI. The Meteorology of Edinburgh. Part III. By R. C. Mossman, 

F.RS.E., F.R.Met.Soc. (With a Plate), . . . .469 

XXII. Vanishing Aggregates of Secondary Minors of a Per symmetric 

Determinant. By Thos. Muik, LL.D., . . . .511 



CONTENTS. Vll 

NUMBER PAGE 

XXIII. Change of Electric Resistance of Nickel due to Magnetisation at 

Different Temperatures. By Professor C. G. Knott, D.Sc, . 535 

XXIV. A Contribution to the Craniology of the People of Scotland. Part 

L, Anatomical. By Professor Sir William Turner, K.C.B., 
D.C.L., F.R.S. (With Five Plates), . . . .547 

XXV. The Generating Function of the Reciprocal of a Determinant. By 

Thomas Muir, LL.D., . . . . . .615 

XXVI. Magnetic Shielding in Hollow Iron, Cylinders and Superposed 
Inductions in Iron. By James Russell, F.R.S.E. (With Six 
Plates), ........ 631 

XXVII. On the Effect of Temperature on the taking of Salmon ivith Rod and 
Fly in the River Spey at Gordon Castle in the Autumns of 1898, 
1899, 1900, and 1901. By George Muirheau, Commissioner for 
His Grace the Duke of Richmond and Gordon, K.G. (With Four 
Plates), ........ 683 

XXVIII. On the Distribution of Fossil Fish-remains in the Carboniferous 
Rocks of the Edinburgh District. By Ramsay H. Traquair, 
M.D., LL.D., F.R.S., Keeper of the Natural History Collection in 
the Museum of Science and Art, Edinburgh. (With Two Plates), . 687 



PART IV. (1903-04.) 

XXIX. On the Applications of Quaternions in the Theory of Differential 

Equations. By J. H. Maclagan-Wedderburn, . . . 709 

XXX. The Lower Devonian Fishes of Gemiinden. By R. H. Traquair, 
M.D., LL.D., F.R.S., Keeper of the Natural History Collections in 
the Museum of Science and Art, Edinburgh. (With Seven Plates), 723 

XXXI. TJie Fossil Plants of the Carboniferous Rocks of Canonbie, Dum- 
friesshire, and of Parts of Cumberland and. Northumberland. By 
Robert Kidston, F.R.S.L. &E., F.G.S. (With Five Plates), . 741 

XXXII. The Canonbie Coalfield: its Geological Structure and Relations to 
the Carboniferous Rocks of the North of England and Central 
Scotland. By B. N. Peach, LL.D., F.R.S., and J. Horne, LL.D., 
F.R.S. (With Four Plates), . . . . .835 



Vlll 



CONTENTS. 



NUMBER 

XXXIII. 



Supplementary Report on Fossil Fishes collected by the Geological 
Survey of Scotland in the Upper Silurian Rocks of Scotland. By 
Ramsay H. Traqttair, M.D., LL.D., F.R.S., Keeper of the Natural 
History Collections in the Royal Scottish Museum, Edinburgh. 
(With Three Plates), ...... 



879 



Elected during Session 1899- 



Appendix — 

The Council of the Society, 
Alphabetical List of Ordinary Fellows, 
List of Honorary Fellows, 
List of Ordinary and Honorary Fellows 

1900, 

Felloivs Deceased or Resigned, 1899-1900, 
List of Ordinary Fellows Elected during Session 1900-01, 
Fellows Deceased or Resigned, 1900-01, 

List of Ordinary and Honorary Fellows Elected during Session 1901-02 
Fellows Deceased or Resigned, 1901-02, 
List of Ordinary Fellows Elected during Session 1902-03, 
Fellows Deceased or Resigned, 1902-03, 
List of Ordinary Fellows Elected during Session 1903-04, 
Felloivs Deceased or Resigned, 1903-04, .... 

Laws of the Society, ...... 

Hie Keith, Makdougall- Brisbane, Neill, and Gunning Victoria Jubilee 

Prizes, 
Awards of the Keith, Makdougall-Brisbane, Neill, and Gunning Victoria 

Jubilee Prizes, from 1827 to 1904, . 
Proceedings of the Statutory General Meetings, 
List of Public Institutions and Individuals entitled to receive Copies of 

the Transactions and Proceedings of the Society 
Index, ...... 



893 
895 
913 

915 
916 
917 
918 
919 
920 
921 
922 
923 
924 
925 

933 

936 
943 

957 
965 



TEANSACTIONS. 



I. — A Contribution to the Life-Histories of the Cod and Whiting. 
By Arthur T. Masterman, M.A., D.Sc. (Lond. and St. And.), F.R.S.E. 

(With Three Plates.) 

(Read 5th June 1899.) 

I. The Cod. 

Considering the abundance of this gadoid, it is a matter for surprise that our know- 
ledge of its life-history is not more complete. The work of Prof. Sars upon the cod in 
Norwegian waters is well known, and need not be referred to in any detail here. It 
is, however, important to avoid the assumption that his account will apply in every 
detail to the cod of British waters. 

In 1883 Prof. M'Intosh * showed that the cod spawned in early spring and that 
spawning was effected outside the territorial limit. Dr Fulton,! from an examination 
of a number of captured specimens, was led to the same conclusion ; and further, that 
the cod, whilst having an extended spawning period reaching from January to June, 
must be regarded as having a main period of February, March, and April, the great 
majority of individuals spawning in the month of March. Thus whilst 40 per cent, of 
the fish examined in March were mature, the proportion fell to 16 per cent, for February 
and April, and 10 per cent, for May. In estimating the growth of this species, by 
the method pursued below, it is probably most correct to regard the true spawning 
period as including the months of February, March, April, and May. A study of the 
distribution of pelagic eggs off the Frith of Forth | leads to a similar conclusion. From 
this latter source the spawning period of the cod can be defined as extending from 

* Trawling Commission Report, 1884. 

t Tenth Annual Report Fishery Board, pp. 232-243. 

t Fifteenth Annual Report Scottish Fishery Board, pp. 222, 223. 

VOL. XL. PART I. (NO. 1). A 



2 DR ARTHUR T. MASTERMAN ON THE 

the third week in February to the second week in May, with a maximum in early 
April. 

The same proofs are to be obtained of the statement that cod, on the East Coast of 
Scotland, spawn some considerable distance from shore outside the three-mile limit, 
Prof. M'Intosh's statement to this effect being corroborated by Dr Fulton in examin- 
ing the distribution of the spawning adults, and by the study of the distribution of the 
eggs. We therefore know that the young larval cod commence their larval history 
floating in the surface water, at or rather near the surface, at some considerable distance 
from land. In the egg and early larval stages they would appear, by the nature of the 
case, to be subject to the physical environment of currents, etc.; but on the assumption of 
the post-larval stage, there is no reason why definite migration on the part of the young 
cod should not be instituted. 

This was pointed out in 1884 by Prof. M'Intosh # in the following terms : — " It is 
evident that the two areas, offshore and inshore, are dependent on each other, and that 
legislation confined to one might not be followed by much benefit. Many inshore 
grounds, for instance, depend on the offing for a supply of the eggs and young of the cod r 
haddock, whiting, coal fish, and pollack ; whilst the offshore is fed by a variable stream 
of the larger young of these fishes from the laminarian region of the inshore." By 
drifting or by definite migration, or possibly by one method succeeding the other, such 
an ontogenetic migration must be effected, for the ordinary habitat of the young cod, 
somewhat over one inch in length, is inshore amongst the rock-pools. In the period 
between hatching and this stage, the young must have effected a migration from the 
offshore pelagic region to the inshore littoral. The details alone of this migration appear 
to require determining. 

Prof. M'Intosh had in his possession a large collection of preserved material, 
extending over several years, and consisting of various gadoids of the post-larval and 
adolescent stages, and has kindly allowed me to go over them with a view to finding 
diagnostic stages in the life-history of some of the gadoids, and, secondly, of elucidating 
their early growth and migration. 

Table I.t contains a list of most of the specimens, arranged in size and order of 
occurrence, which were identified as stages of the cod. It will be noticed that 
there occurs a complete series of young forms, gradating no more than 1 mm. 
between each, from 4 mm. to 46 mm., and that after this another series, varying no 
more than 2 mm., extends to 60 mm. It is quite possible to figure the whole series, 
but only in the very early stages is a repetition at intervals of 1 mm. found necessary - r 
for the young cod, long before it reaches 46 mm., is well known. The stages of special 
interest will be referred to later. The ontogenetic migration must of necessity be 
gradual, and cannot be regarded as passing through its various stages with any absolute 
lines of division. As in most natural phenomena, the majority of the species probably 

* Ifeport Trawling Commission, p. 76. t See note on page 3. 



LIFE-HISTORIES OF THE COD AND WHITING. 3 

conform to a more or less definite sequence, whilst others, tailing* off at either end of the 
average, will constitute the transitional forms. 

For mere convenience' sake, we have in prior papers # divided the habitat into — 
Bottom, in moderate depths, indicated by (B) ; surface-water in offshore and the water 
near the surface, by (S) ; midwater, or the regions of the water extending from about 
two fathoms to the bottom, in moderate depths, by (M) ; and lastly, the littoral district 
and the sea floor therein as (L). 

It is evident that these are purely arbitrary divisions, and, as has been indicated 
elsewhere,t it is not unlikely that physical changes may cause a temporary migration 
from surface to midwater, and even to the bottom. Such changes are known to take 
place in the case of other pelagic forms, and there is apparently no reason why the 
pelagic eggs and larvse should form an exception. This phenomenon, however, does 
not invalidate the demonstration of the true ontogenetic migration, and the eggs, for 
example, of the cod, will still be acknowledged as normally of pelagic surface-habitat 
in spite of the fact that under certain physical conditions some may be found at or 
near the bottom. 

Again, it must be remembered that the division of two fathoms or otherwise between 
the midwater and the surface is a purely arbitrary one, and that hence there are no 
doubt several post-larval forms placed amongst the midwater, which might be more 
accurately located amongst the surface section. 

If the surface-forms, as indicated in Table I.,j be arranged as in Table II., with their 
lengths in mm., forming the abscissae, and the number in each haul the co-ordinates, 
then a distinct curve results. It will be seen that the early post-larval stages, at 4 and 
5 mm., swarm in great numbers in the surface-habitat, and that as growth proceeds, 
there is a steady diminution in numbers till a length of 13 mm. is reached. The 
occurrence of solitary individuals carries the curve on to a length of 17 mm., after 
which the young cod no longer appear at the surface. 

This marked and rapid decrease in number of young cod may be due to several factors. 
Firstly, a great number of them, as development proceeds, forsake the surface-water 
and move downwards through the midwater, where they appear in the diagram under a 
separate curve. Secondly, as development proceeds, the young cod gradually become 
more and more dispersed over the inshore water, so that although the same net was 
employed throughout, and approximately the same districts were worked over, yet the 
number of fishes in each haul steadily decreases, even if we make a combined curve of 
all the four here depicted. At the same time, one can scarcely explain the great 
decrease as being entirely due to a distribution or scattering of the fry, and one is 

* Annals and Mag. Nat. Hist., vol. xvi., Oct. 1895. 

t 14th Annual Scottish Fishery Board Report, 1896 ; loth Annual S. F. B. Report, 1897. 

X The tables were exhibited at the reading of the paper, but have unfortunately disappeared since the work was 
handed in for publication. — P. G. T., Sec. R.S.E. 

Table II. here given is a reproduction of the original to show this graphic method of illustrating the ontogenetic 
migration of food-fishes, and as an explanation of the text. The figures on this table are not absolutely accurate, 
except in so far as they have been taken from the text. — A. T. M., March 1900. 



4 DR ARTHUR T. MASTERMAN ON THE 

inclined to reservedly ascribe a great deal of it to the destructive agencies at work 
amongst the early cod, which we know must take place as a deduction from the high 
fecundity.* 

The midwater curve in Table II. commences with a solitary specimen or two in 
the early 4 and 5 mm. stages, and steadily increases till a length of 9 mm. is 



180 
no 
160 
ISO 
I -to 
'30 
120 
110 
100 
90 
SO 

10 

I 

,60 

j-50 
n 

c 
\20 

10 



zz. 

c 
3 



Table II. 

Cod. 





































































N 






















\ 






















\ 






















\ 






















\ 






















\ 
























\s. 






















\ 
1 
— t 

1 
1 
1 






















1 
— t 

1 
— 1 — . 

1 

1 


M. 




















' •••• 

1 .• 






















V 
























\ 




















: \ 






















:' \ 






















\ 






















> 


• 




















\ 










L. 












\ 






















< 






















^JL 


\ 
\ 


■•. 
















^/ 




x 


^^ 




..••••. 










i 



/J 20 25 30 

— Length s in mmz 
Surface Midwater 



35 



Bottom 



4-0 



4-5 SO 

.Littoral 



55 



reached. From this point to the stage represented by a length of 24 mm., there is- 
a gradual but very steady decrease in the number per haul, a decrease closely parallel 
to that of the surface curve. After 24 mm., from whatever cause, with the excep- 
tion of an occasional isolated specimen at 33 and 38 mm., no more young cod appear 
in the midwater. 

From about 22 mm. onwards there appears the littoral curve. At this size the 



* Natural Science, 1896. 



LIFE-HISTORIES OF THE COD AND WHITING. 5 

young cod are found in the neighbourhood of the shore. Their numbers per haul arc 
seen to increase up to a length of about 33 mm., and then to steadily decrease till 
the curve is carried off the table. An inspection of Table I. will show that the 
littoral forms continue to occur with less and less frequency, up to 134 mm., before 
which size the tow-net is no longer an appropriate method of capture. 

One other curve has to be noticed, namely, that of the bottom tow- net. This 
is at all times very small, although the bottom tow-net greatly exceeds the surface 
net in size of aperture, at least in the case of those captured in St Andrews Bay. 
The curve does not approach that of the midwater net in height, and is mainly carried 
on by one's and two's. Secondly, it will be found that its curve is almost exactly 
parallel to that of the combined curve of surface and midwater. For these reasons 
one is, I think, justified in regarding this curve as due to "incidental" specimens. 
These may occur in two ways. Firstly, a certain small proportion of the surface and 
midwater forms may exceptionally and precociously move to the bottom ; and, secondly, 
the captured specimens may never have been upon the bottom at all. The bottom 
tow-net is a large trawl-like piece of apparatus, and, after its journey along the bottom, 
it is hauled up with open mouth through the midwater and surface. The parallel 
course of this curve to that of the combined surface and midwater curves would favour 
this view, i.e., that it is clue to a series of samples of the surface and midwater regions, 
taken by the bottom tow-net acting as a vertical net upon being hauled up. 

It is quite possible that both the factors above referred to conduce to cause the 
occurrence of young cod in the bottom net, but in either case they would fall under the 
incidental category. They cease to occur after 19 mm., just before the midwater forms 
become littoral. 

In tracing out the ontogenetic migration from these data, we have the two special 
relations of the migration to deal with. 

In a horizontal direction we have the pelagic eggs, as a starting-point, floating in 
the offshore spawning areas. A study of the distribution of these eggs leads us to 
obtain evidence that a large proportion of them drift in towards the shore, and in 
addition, as all the specimens in Table I. have been caught in the districts between the 
spawning grounds and the shore, there is plenty of positive evidence that young cod 
do migrate in the course of development, from the offshore spawning areas to the 
littoral district of the East Coast. Whether others in any quantity migrate seawards,, 
and if they do so, whether they survive and come to maturity, has yet to be proved. 

As regards the vertical migration, the surface curve does not exactly merge into 
that of the midwater net, but from 4 mm. onwards the post-larval cod evidently commence 
to leave the surface water and move downwards into the midwater. The two curves cross 
at about 8 mm., and at about 9 mm. the young fishes occur in greatest numbers per haul. 

From this point onwards to about 18 mm. the surface and midwater forms both 
decrease in number, so that it is improbable that the former owe their decrease mainly 
to a migration to midwater, except in so far as the surface curve decreases more rapidly 



i) DR ARTHUR T. MASTERMAN ON THE 

than that of the midwater. At 23 mm. the decreasing midwater curve is met by the 
littoral, which from here to 32 mm. increases by increments from the midwater, and 
thereafter the results of distribution and of destruction by enemies cause a slow but 
sure decrease. The extreme limits of the surface forms are, from the egg to 1 8 mm. ; 
those of the midwater, from 4 to 39 mm. ; and those of the littoral, from 23 mm. 
onwards. The intersections of the respective curves are at 8*5 mm. and 22 5 mm. 
respectively, and these must be regarded as representing the epochs at which the 
average normally developing cod passes from one division to another. 

It may be noted that the migration downwards from the surface to the midwater 
is more abrupt and effected more rapidly than that from the midwater to the littoral 
region, and this is especially so when it is recollected that growth is more rapid during 
the former period. 

The general facts of this migration have, of course, been well known to scientists 
for several years, but we are further enabled to say that the average cod lives in the 
surface water till a length of 8-9 mm. is reached, when it moves down into the mid- 
water. Here it remains till the proximity of land is reached and it reaches its bottom 
habitat at about 22 to 23 mm. in length. 

There is no evidence in support of the idea that the young cod reach the bottom 
at any great distance from land and then migrate inward along the bottom ; in fact, 
the study of the bottom-net curve in Table II. shows evidence to the contrary. 

The egg and larval stages of the cod have been fully described* and are well known. 
In the St Andrews laboratory the young larva? have occasionally been kept alive 
till all the yolk has disappeared. The length of one of these is given by Prof. 
M'Intosh as 4 mm., and even 4*5 mm. Following upon a description of this stage, 
the same authority describes briefly a number of transition forms which were caught 
in the tow-net. In the present paper several of the stages described by him are figured 
for the first time, and such intermediate stages are added as seem necessary to make 
a complete series from the close of the larval epoch to the young cod of one inch or 
more, from which latter stage there is no difficulty in identification. Fig. 1 represents 
an early post-larval form of 4 '5 mm. (in spirit), probably one of the 5 mm. (fresh) 
specimens noticed by Prof. M'Intosh. The characteristic larval bands of black 
pigment have been reduced to two, which are the two post-anal ones. The ventral 
elements of these two have become fused by the appearance of pigment spots between 
them. A median ventral line of pigment now extends from the anus nearly to the 
tip of the tail. This pigment is superficial, and lies at the base of the marginal fin. 
Dorsally are the upper elements of the two bars and a few scattered pigment spots 
lying over the brain. There is no trace of the two anterior bars. With the addition 
of the intense black pigment of the eyes, this is all the pigmentation discernible in 
.spirit specimens. On the other hand, on clearing, one can readily see a mass of black 

* Trans. Roy. Soc. Edin., vol. xxxv. pi. iii. pp. 812-822. 



LIFE-HISTORIES OF THE COD AND WHITING. 7 

pigment in the peritoneal dorsal wall of the abdomen, especially above the swim- 
bladder, which at this stage is nearly circular. 

When the mouth is closed the mandible forms a very prominent angle, and its 
lower border is very nearly vertical. This character, which is more or less marked in 
most gadoid and other pelagic larvae, is probably to be traced to the method of feeding. 
A gaping mouth at the extreme front end with no inclination upwards or downwards 
would best subserve the capture of pelagic Crustacea, as well as the function of 
respiration. The coloration at this and later stages consists of a diffuse greenish- 
yellow tinge, especially prominent* over the head and back. 

In fig. 2 a length (in spirit) of 5*2 mm. is reached. The external pigmentation 
has increased, the dorsal elements of the post-anal bars approaching one another. A 
few spots upon the mandible and the commencement of a row along the lateral line 
may be recognised. The internal pigmentation has increased, and includes additions 
on the liver and pericardium. This stage carries the series on to fig. 3, in which it is 
evident that considerable progress has been effected. This stage has been described by 
Prof. M'Intosh.1" In the external pigmentation we may notice the first appearance 
of a fine mid-ventral line along the median edge from the anus to the throat. The 
dorsal elements of the two larval post-anal bars have now united to form a median 
dorsal line. Apart from the few scattered spots on the head, the young cod now has 
an external pigmentation of four more or less prominent longitudinal lines, a mid 
dorsal from above the anus to the tail, a mid ventral from the throat past the anus 
to the tail, and a pair of short lateral-line rows in the post-anal portion. Whilst the 
transversely-barred condition of the larval cod is almost unique, this longitudinally- 
barred condition of the post-larval stage, whatever its significance, is of very general 
occurrence in young teleosteans. 

So far as is possible, the pigment of the bars is, as it were, made use of to form the 
lines ; the rest disappears. 

At 7 mm. (spirit), fig. 4, the fin-rays are very evident in the tail, whilst the 
marginal fin is reduced. The external pigment system is similar to that in the preced- 
ing stage, but intensified. A characteristic blotch just behind and over the pectoral fin 
is evident. It is to be noticed that the dorsal and ventral lines do not here, nor at any 
stage, reach actually to the tail, but end suddenly at some distance therefrom. The 
internal pigment is much as before, and tends to spread over the swim-bladder, which is 
still nearly spherical. 

Figs. 5 and 6 carry the series on by easy stages. Increase in intensity of the pig- 
mentation is marked. In fig. 6 the dorsal and ventral lines are very marked, and the 
lateral lines have extended. In this stage the notochord no longer reaches to the tip 
of the caudal fin, which now becomes pronounced in shape. The internal pigment has 
become very dense in the abdominal cavity, and a line extends over the dorsal surface 
of the neural cord. 

* Loc. cit., p. 818. t Loc. cit., p. 818. 



8 DR ARTHUR T. MASTERMAN ON THE 

In both figures the change in inclination of the mandible can be seen, the distance 
from the eye to the tip of the snout becoming proportionally greater. The swim- 
bladder has become oval in shape, and the notochord is less bent in its course dorsally 
to it. A stage closely similar to this (fig. 6) is figured and described elsewhere,* from 
which it appears that in the living condition there are numerous yellow chromatophores 
intermingled with the black, giving the animal a greenish translucence. 

Fig. 7 shows great progress in the acquisition of adult characters, though little 
growth in length has been effected (11 mm.). At about 9 mm., or the length of fig. 6, 
the surface-water is forsaken and the progress through the midwater is gradually 
effected. This alteration in habitat may be correlated with the striking difference in 
structure. The caudal fin is now fully developed, the tip of the notochord, now no 
longer median, being deflected upwards. 

The whole head is cod-like, and the angle of the lower jaw is at about 45° to the 
perpendicular. A minute trace of the barbel has appeared, and a dense mass of black 
pigment covers the brain. The dorsal and ventral lines have moved slightly from the 
median line and are now clearly paired, and the former reaches to the head. The 
lateral line is sharply defined. From the vent forwards the ventral line is small and 
median. Patches of pigment cover the jaws and snout. 

All the adult fins are well differentiated, though still more or less continuous. As 
has already been pointed out, the fin rays of the first dorsal are later in appearance than 
those of the others. A cleared specimen shows the abdominal masses and the supra- 
neural line of the internal pigmentation. 

A whole series of specimens carry us on to the stage in fig. 8, with a length of 19 
mm. It will at once be seen that the changes in external structures effected from 9 mm. 
to 11 mm. are considerably more marked than those which have taken place in the 
growth from 1 1 mm. to 1 9 mm. Beyond the appearance of teeth, the further reduction 
of the tip of the notochord, the further development of the first dorsal and the ventral 
fins, there is little to note. The characteristic external pigmentation is still preserved 
in all its details. The lateral pigment line reaches to the level of the middle of the 
second dorsal. 

A specimen of -ff inch described by Prof. M'Intosh appears to agree very closely 
with the usually occurring stages from this specimen (fig. 8) up to about 22 mm., whilst 
these can easily be followed up through intermediate forms to fig. 9, in which the young 
cod has reached 24 mm. in length (spirit). This would probably be little short of one 
inch long in the fresh state. The head is now unmistakably that of a cod, and whilst 
it is to be noted that the arrangement of the external pigmentation is still very 
constant, apart from the fact that the mid ventral line from throat to anus is no longer 
distinguishable, the proportions have changed. The angle of the jaw has receded to 
well under the eye, and the ventrals have moved forwards. The young fish has at this 

* Loc. cit., pi. xix. fig. 2. 



LIFE-HISTORIES OF THE COD AND WHITING. 9 

stage commenced to take up its littoral habitat, and a rapid development of the external 
pigment will give rise to the well-known ' tessellated ' condition. 

Whilst it is hard to correlate the characteristic pigment lines and markings in the 
early stages with the environment, we are probably justified in regarding the recession 
of the lower jaw and the forward movement of the ventral fins with the adoption of a 
ground-feeding habit. 

If. The Whiting. 

The data for elucidation of the life-history of the whiting are not so abundant as- 
those for the cod, but they are sufficient to enable us to determine, in a general way, 
the form taken by the ontogenetic migration in this case. 

From observations at St Andrews and elsewhere, it has long been known that the 
whiting has a very extended spawning period, from early March to the third week in 
August. A study of the occurrence of the eggs in the Frith of Forth district gave a 
period from the third week of February to the middle of July {Fifteenth S.F.B. Report, 
p. 227). The whiting begins its spawning period at much the same time as the cod. 
but whilst the latter does not extend beyond mid-May, the former continues till mid- 
July. Hence with a spawning period of no less than five months, the young whiting 
caught at any one time might be expected to show great diversity in size. 

A reference to Table III.* will show this to be the case. On 11th July 1895, 
enormous numbers of young whiting were caught off' the Frith of Forth, which ranged 
from 7 mm. in length to 56 mm. The greatest numbers occur at from 15 mm. to 38 
mm., so that they form a maximum in the middle and taper off at each end. This also 
agrees with the facts of the spawning phenomena, and there can be little doubt that we 
have here a case of diversity in size, almost entirely due to a diversity in age, which in 
its turn is due to a prolonged spawning period. Thus, whilst we would be inclined to 
regard the whiting of 7 mm. as a few weeks old, that of 58 mm. might be five months 
old as a maximum. 

The distribution of the eggs and spawning adults both tend to show that the whiting, 
whilst differing in minor features, agrees in general with the cod in its spawning areas. 
The egg is pelagic, and the life-cycle thus commences from much the same starting- 
point as in the case of the cod. 

Up to the present there has been difficulty in obtaining the early post-larval 
stages of the whiting. The larvae appear to be of normal surface-habitat, but on the 
acquirement of the post-larval stage with free locomotion they appear to avoid capture, 
and it is not till the length of 9 to 10 mm. that they are found with any frequency. 
They then occur in the midwater far offshore. This would lead us to suppose that they 
take an opposite course to the young cod, and instead of moving inshore they pass sea- 
wards. Their occurrence in shoals is also very diagnostic. Thus in the table will be 

* See note I on page 3. 
VOL. XL. PART I. (NO. 1). B 



■10 DR ARTHUR T. MASTERMAN ON THE 

seen a small shoal on 28th June, a huge shoal on 11th July, another on 21st July, and 
yet another on 9th August. This peculiar migration of the whiting to the deeper off- 
shore water duriug its earlier post-larval period has been already alluded to by Prof. 
M'Intosh.* Later on, in mid-July, the young whiting commence to move inwards 
" from their retreats in the offshore waters, therefore it is probable that the young 
whiting pass to the inshore waters when between 50 and 80 mm." By September they 
appear in great numbers in the littoral region, frequently the mouths of estuaries, some 
occurring with a length of 130 mm. (or 5 inches). Onwards through the winter they 
occur in increasing size, and on the return of spring they move off to deep water again. 
These facts, already described elsewhere, are confirmed very clearly by the table (Table 
III.).t 

The ontogenetic migration of the whiting would appear somewhat as follows : — The 
surface-water is forsaken at, or near, the close of the larval period and the midwater is 
reached. A migration seawards is then effected into deep offshore waters, where the 
young whiting remains till a length of about 60 mm., when an inshore migration, still 
in the midwater, commences, and the littoral region is soon reached, at an average length 
of about 70-80 mm. 

The oldest whiting which was reared in confinement at St Andrews laboratory is 
figured in pi. xvii. fig. 12 of the Development and Life- Histories of Teleostean Fishes.\ 
A full description of this form is added in the text (p. 825). In this Prof. M'Intosh 
remarks, " so far as present observations go, the young whiting appears to be recog- 
nisable as such when from 9 to 12 mm. in length." The post-larval whiting above 
referred to appears to have been about 23 mm. long, so that there is a considerable 
gap. Figs. 10 and 11 illustrate two specimens caught in the midwater which I would 
tentatively assign to the whiting, though I have grave doubts concerning the propriety 
of so doing. My reasons pro and con will appear in the description. In fig. 10, little 
over 6^ mm. in length, the black pigmentation is sparse. It consists of the usual 
gadoid external mid-dorsal line, more or less separated into two by the median fin, and 
a similar ventral line, but the latter terminates at the anus and the former over the 
swim-bladder, whilst neither extends to the tail. Of the internal pigment, the mass 
overlying the swim-bladder is present, as in other gadoids, and, in addition, there is a 
line of pigment above and below the notochord. There is no trace of pigment either 
upon the head or scattered over the surface of the body. 

The pigmentation of the above-mentioned post-larval whiting is described by Prof. 
M'Intosh in the following terms :— " Black pigment spots arranged in a double 
series along the edges of the muscle-plates, the inner row in each case being somewhat 
fainter. A dense pigment band exists in the sub-notochordal region of the abdomen, 
a,nd scattered spots occur generally over the surface." We may add that the dorsal 
median line is continued forward on to the head, in which region there are also addi- 

* Fifteenth Scottish Fishery Board Report, p. 203. t See note J on page 3. 

J Trans. Royal Soc. Edin., vol. xxxv. 



LIFE-HISTORIES OF THE COD AND WHITING. 11 

tional pigment spots. The two " somewhat fainter " lines appear to correspond to the 
two internal lines in fig. 10 above and below the notochord. These lines are therefore 
common both to fig. 10 and the young whiting, whereas they certainly are not found 
in the cod or green cod. All four lines terminate posteriorly in a similarly abrupt way 
in both the whiting and in fig. 1 0, but the mass of pigment found on the head in the 
former is entirely absent in the latter. In this respect fig. 10 differs from other gadoids 
as well. Lastly, the mid ventral line below the abdomen in the whiting, together with 
several scattered spots on the head, are absent in the form here described. Thus it 
<liffers essentially from the earlier whiting in the absence of several diagnostic elements 
of the black pigmentation. A sojourn for nine years in spirit, with imperfect preserva- 
tion at the outset, may account for a good deal of this. 

Both fig. 10 and fig. 11 are distinctly more advanced than the stages of similar 
length in the cod (cf. with figs. 3, 4, and 5). Thus fig. 10 falls between figs. 3 and 4 
in size, and its mandibular inclination to the perpendicular is, if anything, more than in 
the latter, whereas the oval shape of the swim-bladder puts it on a par with a cod of 8 
mm., with which it is also comparable in the extent of the median dorsal fin and the 
structure of the eye. Fig. 11, which is 7 '45 mm. long, and evidently the same species 
as the preceding, shows even greater contrast with the cod of 8 mm. (fig. 5). In point 
of fact, it is little behind the cod of 11 mm. (fig. 7). 

In the cod of 9 mm. the tail is still perfectly symmetrical though the fin is bifurcated, 
but in this specimen the notochord is deflected and the hypural elements have 
appeared. All the fins but the first dorsal are well formed, and the mandibular angle 
is comparable to that of fig. 7. 

All these characters point, with some probability, to these two specimens belonging 
to a smaller species than the cod, and so far it agrees with the whiting. The poor-cod 
and the bib appear to be the only other possibilities (see below). 

At 9 mm. (fig. 12) the young whiting is clearly distinguishable. The pigmentation 
is very thick and abundant, and its general distribution agrees very exactly with that of 
the larval whiting. The external masses on the head, the dorsal and ventral lines, and 
the internal abdominal masses, are all to be recognised, whilst a dorso-lateral and a 
ventro-lateral line are also present, and a ventral line along the abdomen. 

The fins are continuous, but the positions of the dorsal and anal fins are outlined 
and a certain number of rays may be recognised. Prof. M'Intosh* described a 
whiting of 9 mm., which is at a slightly earlier stage than this specimen. In the 
latter the posterior end of the notochord is bent upwards, which is not the case in the 
former. 

The young whiting of 10 mm. and 11 mm. does not differ in essential features from 
the above. The head becomes rather less prominent and the body becomes thicker, 
obscuring the internal pigmentation. Up to 11 mm. the young whiting has, as remarked 

* Fifteenth Scottish Fishery Board Report, p. 201. 



12 DR ARTHUR T. MASTERMAN ON THE 

by the above author, "more black pigment in the postero-lateral region," and, we may 
add, on the head (cf. figs. 12 and 6), than the young cod of a similar stage. 

At 12 mm. (fig. 13) the ventrals have made their appearance as a minute pair of 
papilla almost exactly below the pectorals. " Groups of black pigment corpuscles are 
distributed alono- the base of the dorsal and the anal fins as well as over the brain, and 
a similar series exists along the median ventral line of the abdomen. Black specks also 
occur along the pre-maxillaries and the mandible" (M'Intosh). ver each side of the post- 
anal portion of the body are finely scattered black specks, which become more prominent 
in slightly later stages. Lastly, there is a series of delicate black bars across the caudal 
rays which make a curved line of pigment on the caudal fin. Fig. 13 is very character- 
istic of this stage, and there is some little change in specimens leading up to 15 and 16 
mm. With increase in size the fins become separated by disappearance of the inter- 
mediate embryonic fin and further growth of the true fin-rays. The posterior tip of the 
notochord disappears and the caudal curve of pigment becomes fainter. The ventral 
fins move slowly forward ; dots of black pigment appear over the median fins and the 
lateral black specks become large and more numerous. These and other lesser changes 
result in a stage, at 16 mm., of the appearance represented at fig. 14. The same general 
distribution of pigment as in fig. 13 can be recognised, and these two figures could not 
fail to serve for the identification of the young whiting from 1 1 to 20 mm. or more in 
length. 

Along with the forward movement of the ventral fin appears that of the anus. 
Thus in fig. 13 the latter is situated immediately below the commencing separation 
between first and second dorsal fin, whereas in fig. 14 it is well below the middle of the 
former. With the forward progress of the anus, the first anal fin becomes longer, and 
new rays are continually added at its front end, so that the 18 of fig. 13 becomes 21 in 
fig. 14, and by the time the stage of fig. 15 is reached, their number has increased 
to 28. 

At about 16 mm. there appears a series of little black touches at the bases of each* 
ray in all the median fins. These are very symmetrical, and are quite distinct from' 
the little specks scattered on the fins between the rays. They are not found in the cod, 
and are absent in the known stages of the haddock. They are, however, of constant 
occurrence in the whiting in every stage, from 16 mm. by gradations of 1 mm. up to- 
25 mm. and beyond. After this they appear to be lost in the general body pigment. 
The caudal curve becomes fainter after 16 mm., and disappears at about 18 mm. 
As will be seen by the accompanying Table, every stage with a gradation of 1 mm. 
from 7 to 25 mm. has been examined, and there is little to note in the way of change 
from 16 mm. onwards. The forward progress of the ventral fins and of the anus, with 
its anal fins, continues, so that in fig. 15 the ventral fins, now elongated, are below the 
occipital region of the head, and the anus is vertically below the first eighth of the first 
dorsal fin. The lateral pigment is greatly increased, and the dorso- and ventrolateral 
lines of fig. 14 have merged into it. At 20 mm. " traces of the median ventral black 



LIFE-HISTORIES OF THE COD AND WHITING. 13 

line are still visible. The black pigment corpuscles along the sides often present a 
more or less longitudinally linear arrangement. No scales are developed. A minute 
papilla in the median line of the mandible indicates a barbel " (M'Intosh). These 
remarks apply with equal force to the 24-25 mm. stage (fig. 15). 

Numerous lesser details may be noticed by a comparison of figs. 13, 14, and 15. 
These three figures should be sufficient to ensure identification at any stage up to 
25 mm. or more. 

From this stage onwards, Prof. M'Intosh thus described the young whiting.* He 
figures the young fish at 26 mm. (pi. vi. figs. 1 and 2), at 30 mm. (fig. 3), and at 
40 mm. (fig. 4), and carries his description up to the stage of 70 mm., after which the 
adult characters are assumed. 

It has already been noted that the early cod is, at the same size, at an earlier stage 
in development than the young whiting. This was evident in the stages up to 9 mm., 
and is strikingly illustrated by a comparison of figs. 1 2 and 6. Again, the figure of a cod 
at 11 mm. may be compared with figs. 13 and 14, and in some respects it is at an earlier 
stage than the whiting of 9 mm. To this rule there is one exception, namely, the 
barbel. This organ can be first clearly made out at about 10-11 mm. in the cod, 
whereas it does not make its appearance in the whiting till a length of 19-20 mm. is 
reached. This is a very marked exception, and one is tempted to connect it with the 
fact that whilst the cod retains its barbel throughout life, in the whiting it is vestigial 
only, and forms an " embryonic " organ. 

Apart from differences in pigmentation, the young whiting from 15 mm. upwards 
can at once be distinguished from the young cod, and probably from all other gadoids, 
by the condition of the anal fin and the forward growth of the anus. The differences 
of external body-form are sufficiently striking, but in this, and especially in the pro- 
portional sizes of various parts, it is very dangerous to draw conclusions from spirit- 
specimens alone. We are safe to notice, however, that the head is proportionally 
larger and heavier in the young whiting up to 25 mm. than in a cod of a similar size, 
the reverse condition holding in the adult. 

Fig. 15 has an outline of the body much nearer that of an adult cod than whiting, 
so that the whiting may be said, in this and other features, such as the presence of a 
barbel, to pass through a " cod" stage. 

Lastly, in pigmentation (black) there are important differences. 

In the larval and early post-larval cod are the transverse bars, diagnostic of the 
species, and the external pigment-line of the lateral line. This appears posteriorly very 
early and progresses forward gradually, and is a constant character throughout the 
stages here described. 

In the whiting, on the other hand, the internal supra-neural and sub-notochordal 
lines, the scattered specks over the fin-membranes and over the post-anal part of the 

* Fifteenth Report Scottish Fishery Board, pp. 202, 203. 
VOL. XL. PART I. (NO. 1). C 



14 



LIFE-HISTORIES OF THE COD AND WHITING. 



trunk, occurring from 1 1 mm. onwards, and the regular dots at the bases of the fin-rays, 
from 15 mm. onwards, are to be specially noted. 

Both species have, in common, the patches on the dorsal surface of the head, the 
internal masses of pigment in the dorsal abdominal wall, the few specks over the 
jaws and the dorsal and ventral external lines, the latter continued forward along 
the ventral surface of the abdomen. These are probably all more or less gadoid 
features. 



EXPLANATION OF PLATES. 



Plate I. 

Fig. 1. Lateral view of post-larval cod 4 - 5 mm. long x about 16 (viewed as transparent object). 
Fie 2 5-2 



x 'o- - 1- >I 


!> »> " " J 


)» >? 


?J ?» )) )i 


Fig. 3. 


6 


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Fig. 4. 


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Fig. 5. 


8 


n a 


M J) )i i) 


Fig. 6. 


9 


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Plate II. 

Fig. 7. Lateral view of young cod 11 mm. long x 11 (viewed as opaque object). 
Fig. 8. 
Fig. 9. 



19 


xlO 


24 


x 10 


Plate III. 





Fig. 10. Lateral view of post-larval gadoid (probably whiting) 6 - 6 mm. long x 15 (viewed as a transparent object). 

Fig. 11. „ „ „ „ „ 7-45 

Fig- 12. ,. „ „ whiting 9 „ x 17 „ 

Fig. 13. ,, ,, ,, ,. 12 ,, x 10 (viewed as an opaque object). 

Fig. 14. ,. young , 16 „ x 10 

Fig. 15. ,, „ „ ,, 24-25 mm. long x about 8 



Trans. Roy. Soc Edin r 

D R Masterman on Larval Cod and Whiting.— Plate i. 



Vol. XL. 

Vnl XXXIX. 











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( 15 ) 



II. — Two Historical Fallacies : Heather Beer and Uisge Beithe. 
By Eobert C. Maclagan, F.R.S.E. 

(Read 8th January 1900.) 

Using Bellenden's translation of Boece, he tells us, "Attoure in all the desertis 
and muris of this realme growis ane herbe, namit hadder, but any seid, richt nutritive 
baith to beistis and fowlis ; specialie to beis. This herbe, in the moneth of July, has 
ane fioure of purpure hew, als sweit as huny. The Pichtis maid this herbe, sum time, 
ane richt delicus and hailsum drink. Nochtheless, the maner of the making of it is 
perist, be exterminioun of the said Pichtis out of Scotland ; for they schew nevir the 
craft of the making of this drink bot to thair awin blud." 

As the Picts left no written records, and as they were exterminated by Kenneth 
MacAlpin, it may be permitted to wonder how Boece came by his information 
[Description of Albion, p. 45). When we come down to Martin, about the year 1700, we 
find [Western Islands, p. 196) that the Picts refused to communicate their information 
to the Scots, "and so 'tis quite lost." In Lightfoot's Flora Scotica, 1777, we find : 
" Formerly the young tops of the heather are said to have been used alone to brew a 
kind of ale, and even now I was informed that the inhabitants of Islay and Jura still 
continue to brew a very potable liquor by mixing two-thirds of the tops of heather to 
one-third of malt." 

The tradition of heather ale has stuck closely to Islay, where it says heather was 
grown for brewing ale. The story in the island is as follows : — 

There are a number of remarkable little plots of ground by the side of the main 
road leading from Bridgend to Loch Gorm, and the remains of old dykes by which the 
plots were enclosed. Local tradition says it was here the Fein had a brewery 
where they made heather ale, and that the small plots were their heather-growing 
grounds. 

Boece's tradition appears in two forms in the island. One is : — 

A man lived in Balinaby who made heather ale for sale. His profits were so great 
that the neighbours wanted to find out the secret, which he would not reveal. At last 
they seized his son and urged him to tell them, but he would not, and they put him to 
death. They next took the father, but he continued obstinate, and they killed 
him also. 

The other form of the tradition points out a flat stone in the old churchyard of 

Kildalton (exactly the opposite side of Islay from Balinaby) which is said to cover the 

grave of a father and his son who were both hanged together at the end of the church. 

This man and his sons were engaged making heather ale, which no one but themselves 

VOL. XL. PART I. (NO. 2). C 



16 MR ROBERT C. MACLAGAN OJN 

knew how to make. Some persons, wishing to find out the secret, bribed one of the 
sons, and the father, to prevent disclosure, with the help of his other son, put him to 
death. For this unnatural deed both the murderers were publicly hanged and their 
bodies buried together in one grave, over which the flat stone was placed. 

Another local legend says that the time of the loss' of how to make heather ale in 
Islay was, when the island was invaded by the Danes. This would make it appear that 
it was to the Danes that the secret was refused, and not to the Scots. 

There are persons who still believe in the possibility of making a fermented drink 
from heather, and even a President of the Royal Society has given the legend a fresh 
lease of life. In the Monastery, Sir Walter Scott says : "Duriug the meal Prince 
Charlie in vain attempted to engage his youthful companion in carousal, or, at least, in 
conversation. Halbert Glendinning pleaded fatigue, and expressed himself unwilling 
to take any liquor stronger than the heather ale, which was at that time frequently 
used at meals." 

In Ireland, on the other hand, on the authority of a gardener from the vicinity of 
Lough Neagh, the Danes get the credit of making the heather beer. It is said there, 
that in cutting turf for peats, when they have stripped off the peat, they find heather 
laid out as if to dry, and it is believed it had been laid out with the intention of using 
it for making beer. 

Heather ale is still manufactured in the north of Scotland, and people tell you that 
they have drank it. I had it on the authority of a lady that she had drank it in Banff- 
shire and found it delicious ; that it sparkled like ginger beer. One writer on Highland 
matters tells that he drank it as lately as 1840, but my lady friend's recollections 
are much less ancient than that. Seeing; then, that it was still in use so short a time 
ago, it seemed probable that some person would have a recollection of how it was made ; 
and a diligent inquirer from a Gaelic source got the following, which seems to have all 
the accuracy one could expect from a practical brewer of it : — 

" Take of the tops of heather as much as is required, put in a boiler, cover with 
water, and boil for three-quarters of an hour. Strain the liquid off, and allow it to cool 
to 70 degrees, add a teacupful and a quarter of yeast to the gallon of liquid, put in a 
crock or cask, covered with a cloth, and in two days it may be bunged down." 

The quality of the heather, however, seemed to require a greater accuracy of descrip- 
tion. The reciter was again interviewed, and said that the heather required to be gathered 
when in bloom, that the boiling was continued according to the strength of infusion 
required, but that there was no other test but that of the individual taste of the operator. 

Now, as Martin told us that in his day the heather was mixed with malt, the 
question was put whether or no sugar was used, and he said " No," there was enough 
sugar in the heather. This reads, according to subsequent knowledge, like a mere tissue 
of falsehood, and yet I believe it was merely a repetition of a traditional story, though 
where the 70 degrees came in is a little hard to diagnose. 

Heather honey is known to us all, and it seems quite natural that an infusion of 



TWO HISTORICAL FALLACIES : HEATHER BEER AND ITISGE BEITHE. 17 

that honey-producing plant should be fermentable. Indeed, the extract from Boece in 
which he calls attention to the liking for heather by " beis" seems to indicate the origin 
of the tradition. The locality of inquiry, then, was changed to the inland north of 
Scotland, where there could be no doubt that an acceptable fluid had been quite recently 
used under the title of heather beer. And from Miss Paull of the Manse of Tullynessle 
was got a recipe from "a woman who makes it often, says it is very good and supposed 
to be very strengthening." Here is the recipe : — 

\ peck of malt. 

1 oz. hops. 

3 gallons of water. 

Twa guid gowpenfu's of heather blossom. 

1 lb. sugar or treacle. 
Small teacupful of yeast. 

Put the malt, hops, and heather blossom in a bag, and boil in the water for two 
hours. Add the sugar or treacle and strain ; let it stand till lukewarm, then add the 
yeast. Let it stand till the third day, skim it, and then bottle it. The malt may be 
omitted if preferred. If the ale is wished sweet, more sugar must be added. 

As the user of this recipe was quite willing to make some, I got a few bottles as a 
sample. It was not well brewed, was exceedingly sweet, and certainly had a curious 
taste, no doubt the result of the heather added to it. In fact, it was a poor sample of 
sugar beer with heather instead of ginger. 

The heather employed was to be gathered in full bloom, was to be by preference not 
bell heather, and might be kept some time before using. 

Another authority, who hails from Glen Urquhart, was equally positive that there 
they used " deep heather, the under part of the stems, bits that have not got the sun. 
You simply boil it a long time, sweeten it with syrup or sugar, add barm, and bottle it." 

Finally I got a recipe, holograph, of the manufacturer : — 

2 lbs. of heather bloom. 
5 lb. hops. 

2 oz. ground singer. 

3 lbs. syrup. 

Boil all together in 2 gallons of water for half an hour. Strain and add other 2 
gallons of water, and when it is cold as new milk, add half a cupful of barm. Cover it 
up for twelve hours. Skim the top, pour it off gently to keep the barm that has sunk 
to the bottom, then bottle and cork firmly. 

There is a reason for confusion between the heather top, that is the flowering stem of 
the heather, and the heather bloom, as both in Gaelic are called barr. 

All my first information pointed to the use of the heather top, and so I collected 
with considerable care a quantity of the finest flowering stems of the common heather I 



18 MR ROBERT C. MACLAGAN ON 

could get. These were subjected to analysis for sugar in the laboratory under the care 
of Dr Huntkr Stewart. 100 grammes were digested for six hours in streaming steam 
100 c. 

The total bulk of the decoction so made was 1500 cubic centimetres. It contained 
•1G(>6 per cent, glucose. Another 100 grammes yielded 2 - 49 grammes glucose. These 
results show, then, that, decocted with steam, carefully selected heather tips yield 
practically 2\ per cent, glucose. This seemed to give colour to the traditional possibility 
of fermenting a decoction of heather flowers. 

Seeing, however, that the bees gather their honey from the flower itself, and not 
from the stick, a quantity of the bloom, as free as possible from all contamination with 
woody matter or leaves, was analysed at Gran ton, under the superintendence of 
Mr Irvine, with the astonishing result that it yielded 17 per cent, of a substance 
which reduced Fehling's solution, and which by ordinary tests would appear to be sugar. 
To put this practically out of doubt, a decoction was made and yeast added to ferment 
it. The result was a negative one ; there was no alcoholic fermentation and no dis- 
engagement of carbonic acid, so that there was no evidence of fermentable sugar being 
present in any proportion. 

Having failed in the laboratory, it seemed advisable to have a trial made by a 
practical brewer, and Mr Andrew Melvin of the Boroughloch Brewery willingly 
undertook the experiment. 

I supplied him with a quantity of pure heather blooms. He extracted 4 lbs. of this 
with 6 gallons of water. To give an idea of the bulk of the heather flower, 2 oz. very 
nearly equalled the bulk of one and a half imperial pints. 

To the extract obtained yeast was added ; at the end of ten days a fresh supply of 
yeast, artificial warmth being maintained and the cask well rolled. There was no 
appearance of fermentation. I examined it myself two days later, and its condition 
was unaltered. The fluid was of a fine dark beer colour, perhaps a little more 
inclined to red. When drawn from the top, it was bright and showed about 1^- 
degrees of the saccharometer, a slight shade higher than before the yeast was added, 
which Mr Melvin suggested might have arisen from a little wort adhering to the pressed 
yeast. 

When the extract was first made, it had a marked woody flavour, but after the treat- 
ment above described this had entirely disappeared. This seems quite a satisfactory 
experiment from a brewer's point of view, and proves that a fairly strong infusion of 
carefully picked heather flowers will not ferment. This entirely agrees with the 
Granton laboratory experiment, which we should note was made alongside a solution of 
grape .sugar of the same proportions as the pseudo-glucose, the grape sugar fermenting 
while the heather infusion remained unaltered. 

Mr Melvin's extract was made in a copper jacket pan. The heather was added in 
two quantities, the brewer conducting the experiment thinking that the first quantity 
added was not sufficient. When I examined it, it had a perceptibly worty smell. It 



TWO HISTORICAL FALLACIES : HEATHER BEER AND UISGE BEITHE. 19* 

had no sweet taste, nor was thick in the mouth, nor indeed had it any special taste 
which one could be led to connect with the presence in it of heather flowers. 

As we could not ferment a decoction of heather flowers, it seemed right to settle 
whether a decoction of malt could be fermented with heather. Some malt wort had 
heather flowers added to it and was carefully handled in the Boroughloch Brewery, in 
hopes that a good result would be got. After six days there was no appearance of an 
alcoholic fermentation, the heather blooms themselves were covered with a green mould 
where they floated upon the top of the wort, and the smell was by no means pleasant, a 
certain quantity of acetous fermentation being evidently present. After examining the 
sample myself it was corked and kept in a warm place, but no alcoholic fermentation 
took place. 

It is difficult to believe that anyone who has repeated these stories ever made even 
a simple infusion of the flowers and tasted them. Such an infusion as strong as it can 
be made smells of the heather tops, but its taste is slightly bitter, with what one might 
describe as a leathery flavour ; it is not in the least degree sweet, as would be the case 
if it contained any quantity at all of glucose. 

Having now proved that beer could not be made from heather alone, and that the 
heather was not of itself a ferment, and regarding the recipes for heather ale which were 
the results of practical experience, Mr Melvin and I came to the conclusion that it could 
do nothing else, if it had any value at all, but act as a flavouring matter and preservative 
like hops. Mr Melvin then made the following experiment : — 

Four gallons malt wort, sp. gr. 100, with four gallons of water, were boiled with 
heather flowers, total quantity being 1\ lbs. The mixture was strained and the filtrate 
boiled for another half hour. The fluid smelt strongly of heather, and had an agreeable 
taste. It was now rapidly cooled to expose it as little as possible to air germs, and at a 
temperature of 69° Fahr. was poured into a 6-gallon cask, the quantity being made up 
to fill the cask of cooled boiled malt wort, and a pint of yeast well mixed into it. As 
it worked, the cask was kept carefully filled so as to allow the yeast to work thoroughly 
out of the beer. For the first twenty-four hours the fermentation was active and had 
an agreeable smell. When the fermentation was complete, the heather beer produced 
was bottled, and the result, though not perhaps adapted for exhibition, was a fairly 
potable liquor, with a roughish woody flavour peculiar to itself, and no doubt the effect 
of the heather which had been put into it. Before bottling, however, a sample was 
taken of the yeast from the latter workings and microscopically examined. The yeast 
cells were well defined, healthy, and vigorous-looking, but the field was decidedly 
impure, bacteria being present in such alarming quantity, from a brewer's point of view, 
that the beer's keeping quality was very doubtful. It was accepted that these bacteria 
came chiefly from the heather, as the yeast used was a very pure sample. Mr Melvin 
was of opinion that we had used too little heather for even such a small quantity as 
6 gallons, and it was determined to make another brewing with fresh heather, guided 
by the experience already gained. In the following year, then, this intention was 



20 MR ROBERT C. MACLAGAN ON 

carried out, and a cask of heather ale of a highly satisfactory appearance was 
prepared and ready for bottling. Then the brewery unfortunately took fire, 
and afterwards all that was found of the heather beer that could be recognised 
were two hoops of the barrel and some charred staves. It had been fined and 
stacked with some special samples, of which as little remained. As the question 
was not one of flavouring malt, but of fermenting heather itself, and it being 
clearly proved that this was impossible, it was unnecessary to make further experi- 
ments. Nor has the result of our trials led Mr Melvin to introduce to his consumers 
heather ale. 

The truth is that the heather harvest is troublesome and not productive. To 
gather a pint of the flower, carefully stripped from the stalk, takes about one hour 
of diligent work. One of my gatherers was of opinion that the man who suffered 
martyrdom rather than tell the secret of how the heather ale was made deserved 
a monument by a, grateful posterity. If the few bottles of beer we had got caused 
so much labour and expense, to what would it have been possible to compare the 
slavery of those unfortunate wives from whom their lords demanded it in bucketsful ? 

The whole story of heather beer has, I should fancy, arisen from a pre- 
conception as to the presence of honey in the heather flowers as we know it 
in the comb. The experiments so far go to prove that honey as such does not 
exist in the flower, and that bees are something more than mere gatherers so far 
as honey is concerned ; but if the heather flower is extracted with ether the residuum 
on evaporation is ordinary beeswax, showing that this product exists already before 
gathering. 

How misconceptions arise was proved by one who, seeing the heather being gathered 
and asking what it was for, said, " I will tell you who made heather ale not long ago : 
Mrs J. of E." " Who told you ? " " Dr J., her son, was bad with asthma, and it is used 
as a cure for that." 

As Dr J. was a professional brother, I took the liberty of writing to try to get at 
the bottom of the matter, and in a few words it turned out that from a paragraph in a 
paper, which stated that heather tea was a cure for asthma, A. had been dosed with it 
even by his own account with but little perceptible benefit. A. says that whether it 
would make beer or not he does not know, but that it was bitter enough to act, if it 
acted at all, as a tonic. 

It was suggested that, by oxidation or other changes induced after plucking, the 
fermentable honey in the heather flowers might have altered. To see if this 
could possibly be the case, an attempt was made to ferment a decoction made of 
heather flowers gathered within thirty-six hours. There was no more evidence of fer- 
mentation under these circumstances than when the flowers had been kept for some time. 

Further, to exclude any source of error in a statement that heather will not make 
ale in any way, experiments were made with a solution of honey, gravity by saccharo- 
meter 1056, to try if old blooms, or perfectly fresh, would act as a ferment in what 



TWO HISTORICAL FALLACIES: HEATHER BEER AND UISGE BEITHE. 21 

might be considered their natural sugar. Neither gave, any evidence of fermentation,, 
while a parallel experiment with the same honey solution and ordinary yeast fermented 
successfully. 

A supposititious and fabulous stimulant is also said to be procurable from the sap 
of the birch tree. So convinced are many persons of the possibility of the forma- 
tion of such a liquor that the} 7 maintain that the Gaelic for whisky, uisge beatha, 
aqua vitae, is a corruption of uisge beithe, birch water. Hooker, in his British Flora,. 
informs us that a wine is made from Betula Alba in Scotland, and other authorities 
speak of its rich, sugary, plentiful spring sap which makes a beer, a wine, and a vinegar. 

As in the case of heather beer, the use of this sap is referred to old times. "At a 
very remote period Highlanders made incisions in birch trees in spring, and collected 
the juice which fermented and became a gentle stimulant " (Paper by a Supervisor of 
Excise, Celtic Magazine, vol. xi. p. 381). "Most of us when boys have had our 
favourite birch tree, and enjoyed the Jion, wine." 

A small matter delights boys. A native of Killin, in Perthshire, says that they 
made fissures in birch trees and sucked the juice with their mouths. One fissure would 
yield enough for a whole day. He used to go back and back to it. A deeper and wider 
hole was scooped at the bottom of the cut in which the sap accumulated. Others 
again peel the bark and scrape off and chew the white inner bark, which is very sappy. 
This goes by the name of Snothach, which simply means the sap. Lightfoot gives the 
following recipe, which, however, falls back on sugar for the source of the alcohol. He 
settles the question of self-fermentation by hard boiling. He says : " In the beginning 
of March, when the sap is rising, and before the leaves shoot out, bore holes in the 
bodies of the larger trees and put fossets therein, made of elder stick with the pith taken 
out, and then put any vessels under to receive the liquor. If the tree be large you may 
tap it in four or five places at a time without hurting it, and thus from several trees 
you gain several gallons of juice in a day. If you have not enough in one 
day, bottle up close what you have till you get a sufficient quantity for your purpose, 
but the sooner it is used the better. Boil the sap as long as any scum rises,, 
skimming it all the time. To every gallon of liquor put four pounds of sugar and 
boil it afterwards half an hour, skimming it well ; then put it into an open tub to 
cool, and when cold run it into your cask ; when it has done working bung it up 
close, and keep it three months. Then either bottle it off or draw it out of the 
cask after it is a year old. This is a generous and agreeable liquor, and would be a 
happy substitute in the room of the poisonous whisky" (Trans. Gael. Soc. Inv., 
vol. vii. p. 136). 

This is one of the most imaginative prescriptions with the circumstance that has 
been written. The generous liquor can only have been simple syrup. 

The method of gathering the sap, and the knowledge shown of the time for doing 
so, limits exactly the practical knowledge of Lightfoot s informant. The birch sap does 
not run when the leaf begins to bud : that is evidence of the cessation of the flow. 



22 TWO HISTORICAL FALLACIES: HEATHER BEER AND UISGE BEITHE. 

Samples were got from the central district of Perthshire and from the island of Islay 
for purposes of analysis. The Islay sending was first to arrive. On drawing one of the 
bottles and tasting it, it was so entirely free from taste of any sort, and so limpid, that 
the conclusion was at once formed that rain water had been supplied, and gave the 
credit to the friend acting as a collector of playing a trick, but on inquiry the forester 
who had gathered it, a thoroughly reliable man, described precautions to prevent any 
dilution by rain, and was prepared to guarantee that the sap was free from mixture of 
any kind. An analysis was then made in the Public Health Laboratory in the 
University, reported as follows : — 

" It was slightly opalescent, with a faint acid reaction. Its specific gravity was 1002, 
water 1000. It contained no sugar, its total solids being 0*302 per cent. The solid 
matter was almost entirely vegetable albumen, and contained neither starch nor dextrine." 

The Perthshire sample arrived in Edinburgh in the beginning of April, which 
accurately corresponds with the time of the year mentioned by Lightfoot as the best in 
which to gather it. It was very carefully analysed at Granton. It was also slightly 
opalescent, and it was impossible to filter it clear. At 59° Fahr. it had a specific 
gravity of 1003*09. It yielded on evaporation over the water bath 0*6910 solid 
matter per cent. On examination this was found to consist of extractive matter 5 420 
per 1000 grammes (or grammes per litre) ; fermentable sugar, 0*440 per 1000 ; tartaric 
acid, 0*455 ; ash, lime, magnesia, and alkalies, 0*290. 

In addition to the solid matter there was a small quantity of alcohol present, 0*244 
per 1000; carbonic acid, 0*293 per 1000. 

This alcohol must have been the result of a natural fermentation of the sugar in the 
sap, and allowing for this, the amount per cent, of sugar in the sap, including what had 
been fermented naturally, and what was fermentable, was 0*680 grammes per litre, or 
0*0680 per cent. 

The determination of the sugar was made by fermentation with dry German yeast ; 
the tartaric acid by the silver mirror. The extractive matter was found to reduce 
copper, but only being fermentable to the small extent mentioned, we may conclude 
that the most of it was dextrine ; this, however, does not agree with the first analysis, 
which gave no sugar, nor starch, nor dextrine, and consequently the whole was supposed 
to be vegetable albumen. 

From a practical point of view, and granting what is possible, that samples of birch 
sap may vary in the richness of their contents, it never could of itself yield anything 
active either as a drink or as a medicine. Lightfoot's recipe would come out probably 
quite the same if so much water were used in place of the sap. 

In fact, the conclusions reached are, that though heather flowers, if infused in malt, 
or added to a fermentable syrup, may give a flavour to the product, it is in itself of no 
value as a source of ale or beer. 

Birch sap is equally useless, and can only give satisfaction as a drink or a medicine 
from an imaginative point of view. 



( 23 ) 



III. — On the Eliminant of a Set of General Ternary Quadrics. — (Part II.) 

By Thomas Muir, LL.D. 

(Read December 4, 1899.) 

(26) Of the various determinant forms thus far obtained the most promising is that 
of § 8 or that of §14; and to these it is desirable now to return in order to obtain an 
expression for the eliminant in the ordinary non-determinant notation. In doing so it 
will also be well to make a slight change in the coefficients of the three quadrics, viz., 
to write f g, h for 2f 2g, 2h, as in this way the diversity in the cofactors of the deter- 
minants occurring in the last three rows of either form of the eliminant disappears. 

Using first the result of § 8, we have therefore as the eliminant of 



the determinant 



where 



a x x 2 + b t y 2 + c x z 2 + f$z + ffjZX + \xy = v 
a 2 £ 2 + hgj 1 + c# 2 4- f 2 yz 4- g$x + h 2 xy = > 
a s x 2 + b.^ 4- c 3 2 2 4- f0z + y. d zx + \xy = ) 



a x 


\ 




h 


A 




9x 


*1 


a 2 


h 




o-i 


A 




9>2 


K 


a. A 


h 




C 3 


A 




9 S 


i h 




[5] 


- 


[31 


[8] + [81 


[6] 


[0] 


-[1] 


. 




[6] 


[0] 




;9]+[9'i 


[41 


[4] 


"[2] 




• 


[5] 




[0] 


[7] + [7'] 






[0] 


— 


1 <h h 2 C 3 1 












[1], [2], 


[3] 


= 


! O^jAg | 




1 \KA 1 


, 1 c iA9z ' 


> 




[41, [51, 


[6] 


= 


| Ojft^g | 




i x c. 2 h s \ 


, | ^^2/3 


, 




[7], [8], 


[9] 


= 


1 oA/s 1 




1 W 8 \ 


, I.C^g | 


j 




[7'], [8'], [9'] 


= 


1 hffA 1 




1 c AA 1 


; 1 a iJ29z 1 





Now, as the minors formed from the first three rows of this determinant of the 6th 

order are the set of twenty to which belong the thirteen determinants appearing in the 

other three rows, it follows that if we take the expansion in terms of minors formed 

from the first three rows and their complementaries, we shall obtain for the eliminant 

an expression consisting of terms each of which is the product of four of the twenty 

determinants [0], [1], [2], .... Doing this, and bearing in mind the existence of 

triads due to the cyclo-symmetry, we have as a preliminary form of the development 
VOL. XL. PART I. (NO. 3). D 



24 



DR THOMAS MUIR ON THE 



[0] 



[8] + [8'] [6] 



[0] 



[0] 
[5] 



-2[7] -[3] 
[6] 



+ SL9'] 



-[0'] 



[9] + [9'] [4] 

[o] [7]+ mi 

[6] [0] 

[9] + [9'] [4] 

[0] [7] + [7'] 



+ 1[4] 



■[3] [8] + [8'] [0] 
[6] [0] [4] 

[5] [7] + [7'] 



[5] 


-[3] 


[0] 


- Z[4'] 




[6] 


[4] 




-[2] 


• 


[7] + [7'] 






[5] 


-[3] 




-[1] 


. 


[6] 




[4] 


-[2] 







[5] 
-[2] 



■[3] 
[6] 



[6] 

[9] + [91 

[0] 



- Z[io] 



+ Z[l] 



-[3] [8] + [8'] [6] 
[6] [0] [9] + [9'] 
[5] [0] 

[5] -[3] [8] + [8'] 
[6] [0] 

-[2] • [5] 



The development of the first of these eight terms, if we agree to drop the rect- 
angular brackets in [0], [l], . . . . , 

= 0(8 + 8')(9 + 9')(7 + 7') + 0000 + 0456 - ±004(8 + 8'), 

= 0789 + 0897' + 089'7 + 0897' + 08'97 + 08'97' + 08'9'7 + 08'9'7' + 0000 + 0456 \ 

- ±0048 - ±0048' j , 
= 0789 + ±0789' + ±078'9' + 07'8'9' + 0000 + 0456 - ±0048 - ±0048'; 

that of each of the others is directly evident ; and the coHected and simplified whole is 



0000 
+ ±00111" 

-±0048 - ±0048 
-±0048' 
+ ±0123 

-±0158 - ±0158 
+ ±0456 + 0456 
-±0456' 
+ ±049lT 
+ ±04911 
+ 0789 
+ ±0789' 
+ ±078'9' 
+ 07'8'9' 
+ 0123 
- 0'456 

(27) Taking now the result of § 14, viz., 
a, &, c, 



+ 21268 

+ ±1268' +±1268' 

-±126'8 

-±126'8' 

+ ±1556 +±1556 

-±1556' 

-±16711 

- ±16711 
+ ±1788 
+ ±1788' 
+ ±17'88 
+ ±17'88' 
+ ±4488 
+ ±4488' 

- ±44611 
-±4589 
-±4589'. 



a 3 

9 

-1 



h 

-2 



A 

A 
A 

5-5' 
8 




<7i 

ffs 


6-6' 

9 



h 2 

K 

7 



4-4' 



ELIMINANT OF A SET OF GENERAL TERNARY QUADRICS. 



25 



and expanding in exactly the same way, we have 

0000 +±1268 

+ ±00111 -±126'8 - 

-±0048 - ±0048 +±1268' 

+ ±004'8 -±126'8' 

+ ±0123 +±1556 

-±0158 - ±0158 -±1556' 

+ 0456 -±155'6 

-±0456' +±155'6' 

+ ±045'6' -±16711 

- 04'5'6' +±16711 
+ ±04911 +±1788 + 
-±04'9lT +±17'88 

+ ±0789 + 0789 +±4488 

+ ±0789' -±44'88 

- 0'789 -±4589 
+ 0123 +±4'589 



±126'£ 



•±77812 



(28) The terms common to the two expressions are 



0000 




. +±1268 


+ ±00111 




-±126'8 


-±0048 - 


±0048 


+ ±1268' 


+ ±0123 




-±126'8' 


-±0158 - 


±0158 


+ ±1556 


+ 0456 




-±1556' 


-±0456' 




- ±16711 


+ ±04911 




+ ±1788 


+ 0789 




+ ±17'88 


+ ±0789' 




+ ±4488 


+ 0123 




-±4589. 



±1788 



The remaining terms in each case are fourteen in number, and of course the aggregate 
of the one group must be equal to the aggregate of the other : that is to say, it must be 
possible to show that 



-±0048' 


±004'8 


+ ±0456 


+ ±045'6' 


+ ±04911 


- 04'5'6' 


+ ±078'9' 


-±04'911 


+ 07'8'9' 


+±0789 


- 0'456 


- 0789 


+ ±1268' 


-±126'8 


+ ±1556 


-±155'6 



26 DR THOMAS MUIR ON THE 



-2167'IT [ = ] 


+ 2155'6' 


+ ±1788' 


+ ±16711 


+ ±17'88' 


+ ±1788 


+ ±4488' 


-±44'88 


- ±44611 


+ ±4'589 


-±4589 


-±77812. 



Fortunately the process by which this is accomplished brings to light a simpler expres- 
sion than either of the two. 

(29) In the first place it can be shown that the aggregate of the first two terms on 
the left is equal to the aggregate of the first and fifth on the right, the single term 
±04911 being an equivalent for either. As a matter of fact, we have, by a well-known 
elementar) 7 theorem, 

«A C 3 1 • I C AA ! = I Khh I • I c i a ?A i + I a A c s I • I c A/s I . 

i.e., 08' = 56-911, 

and therefore, on multiplying by — 04, 

-0048' = -0456 + 049TT, 
and consequently 

-±0048' + ±0456 = ±04911; 

and the fact that 

±004'8 + ±0789 = ±04911 

follows in exactly the same way from the identity 

04' = 6l0 - 79 . 

(30) There are four other pairs of identities like this, the full collection being 

-±0048' +±0456 = ±04911 = ±004'8 +±0789, 

±04911 - ±44611 = -±47TTl2 = -±04'9lT - ±77812, 

±1556 +±4488' - ±44611 = ±045'6' + ±4'589 , 

±078'9' -±4589' = -±77812 = ±1788 - ±44'88, 

±1268' + ±17'88' = ±16'7'IT = -±126'8 + ±155'6'. 

Further it can be shown that 

-±16711 + ±1788' = ±16711 - ±155'6; 



ELIMINANT OF A SET OF GENERAL TERNARY QUADRICS. 27 

but unfortunately in this case there is no simple equivalent which can be substituted for 
either. This difficulty, however, can be overcome by taking one of the terms common 
to the two original expansions, viz. ±1268, and adding it to each side, for then we have 

-±16711 + ±1788' + ±1268 = + ±16711 - ±155'6 + ±1268, 

= -±16711 + ±16711. 

It is thus seen that in each of the original expansions an aggregate of thirteen terms 
may be supplanted by an aggregate of seven, viz. 

±04911 - ±471112 + ±44611 - ±77812 + ±16711 - ±16711*+ ±16711*; 

and that it only remains to prove the equality of 

07'8'9' - 0'456 and -04W - 0789 , 

and if possible to find for either of them a simpler equivalent. 
Beginning with the left-hand side we derive from 

07' = 45 - 810 , 0'6 = 8'9' + 34', 

in the same manner as before the identities 

±07'8'9' = ±458'9' - ±88'9'T0 , 
-±0'456 = -±458'9' - ±344'5 , 

* For each of the terms 2l67'll, 2l6'711 an alternative form is available, by reason of the existence of a curious 
kind of identity of which there are three instances, viz. : — 

2l67'TT = 2l59'TT, 

o o 

2i6'7iT = 2i48'iT, 

S44'88' = 24'589' . 

The mode of establishing these may be illustrated by proving the last of the three. 
By a well-known theorem we have 

I a AU I I c i% 3 1 = ! s'A/s i I <hK a s I + i c hy-ifs ! I c i h A I + I a i & 2</ 3 1 I c A/ 3 1 . 

i.e., 76' = 5'9 - 9'5 + 48', 

or ' 76' - 95' = 48' - 59', 

where, be it observed, each side consists of two terms of a triad. Multiplying, then, both sides by the remaining term 
of either triad, say by 84', we have 

84'(76'-95') = 84'(48' - 59') , 
and therefore by cyclical substitution 

95'(84'-76') = 95'(59' - 67') , 
and 76'(95'-84') = 76'(67' - 48') . 
From these by addition there results 

= 284'48' - E84'59' 
or 24'589' = 2°44'88'. 

The three fundamental identities which can be treated in this manner are 

76' - 95' = 48' - 59' = 1 11 - 2 12, 
or, of course, their derivatives by cyclical substitution. 



28 DR THOMAS MUIR ON THE 

and therefore by addition obtain 

±07'8'9' - ±0'456 = -±88'9'10 - ±344'5 , 
= -±77'8'12 - ±155'6. 

Again, from the identities, 

06' = 512 - 89, 07 - -29' + 4'5', 
we derive 

-±04W = -±4'5'512 + ±4'5'S9, 
-±0789 = ±2899' - ±4'5'89 , 

and thence by addition 

-±04'5'6' - ±0789 = -±44'6'lT + ±1788'- 

Now the two alternative forms thus obtained, viz. 

-±77'8'12 - ±155'6 , - ±44'6'11 + ±1788', 

though no simpler than the original, are readily seen to be equal, because 

±1788' + ±77'8'12 = ±4678' = ±4'589' 
and 

- ±44'6'll - ±155'6 - ±5'67'9 = ±4'589'- 

(31) The simplified form of the eliminant to which we are thus led contains twenty- 
one of the twenty-two terms given in § 28 as being common to the two original expan- 
sions, and nine others which take the place of the fifteen remaining ; and if, further, we 
substitute for - ±0456' -±4589 its equivalent -±44611, we have finally 



0000 




-±126'8' 


+ ±00111 




+ ±1556 


-±0048 - 


-±0048 


-±1556' 


+ ±0123 




- ±16711 


-±0158 - 


-±0158 


-±167'IT 


+ 0456 




+ ±16711 


+ ±04911+ ±04911 


+ ±167'iT 


+ 0789 




+ ±1788 


+ ±0789' 




+ ±17'88 . 


+ 07'8'9' 




-±44611 


+ 0123 




+ ±44611 


- 0'456 




+ ±4488 


+ ±1268' 




- ±471142 


-±126'8 




-±77812. 



ELIMINANT OF A SET OF GENERAL TERNARY QUADRICS. 29 

Possibly there may be found modifications of this expression which are at least 
equally compact. There certainly will be unlimited variety if the number of terms be 
not restricted as here, since for almost every one of the terms a substitution of two or 
more similar terms is possible. The only terms, indeed, which cannot be replaced are 
0000, -220048, ±4488. 

(32) Leaving now the subject of these eliminants of high order, — a subject which, 
as we have seen, originated with Sylvester, — let us ascertain what is possible in the 
direction of attaining the eliminant in the form of a determinant of an order lower than 
the sixth. 

In one of the special cases already referred to it has been shown * that from the three 
original equations in x 2 , y 2 , z 2 , yz, zx, xy we were able to deduce a set of three in 
yz, zx, xy, a set in x 2 , y 2 , z 2 , and a set in x, y, z, and thus to obtain expressions for the 
eliminant in the form of a determinant of the third order. That is to say, instead of 
having in our equations all the possible facients of the second degree, viz., both those of 
the type x 2 and those of the type yz, we succeeded in confining ourselves to equations 
having only one type of facient. 

In the same case it was also shown that there could be deduced a set of four equations 
in x 2 y, y 2 z, z 2 x, xyz ; a set in xy 2 , yz 2 , zx 2 , xyz, and a set in x 3 , y 3 , z 3 , xyz : and that in 
this way expressions could be obtained for the eliminant in the form of a determinant 
of the fourth order. Here, where the facients are of the third degree, there are 
four types of them, x 3 , x 2 y, xy 2 , xyz ; and Sylvester, just as in the case of the 
facients of the second degree, used the whole of them and thus saddled himself 
with a determinant of the tenth order. The reduction to the seventh order made 
in § 1 was due, it may be noted, to the elimination of one of the four types, the set 
of facients implicitly retained being x 2 y, y 2 z, z 2 x, xy 2 , yz 2 , zx 2 , xyz. 

We shall now see whether the processes applied to this special case can be extended 
to the general problem at present before us. 

(33) When the set of facients does not possess the cyclo-symmetry apparent in each 
of the sets just spoken of, it is scarcely reasonable to expect that the resulting eliminant 
will be simple or elegant in form. If, therefore, we seek to obtain the eliminant as a 
determinant of the fifth order — a course which would necessitate the use of a set of 
facients like y 2 , z 2 , yz, zx, xy, or x 2 , y 2 , z 2 , yz, zx, — we must be prepared for more or less 
irregularity and complexity. It will be found, nevertheless, that this fifth-order form 
is full of interest. 

Taking the set y 2 , z 2 , yz, zx, xy, we examine our collection of derived quaclrics having 
co-efficients of the third degree, viz. : — 

[Table 

* Muir, T., " Further Note on a Problem of Sylvester's in Elimination," Proc. Roy. Soc. Edin., xx. pp. 371-382. 



30 



DR THOMAS MUIR ON THE 



Source. 



u Af:i I 

u l e i g. i | 

U \ a J l 3 
T^Cgfig I 

U l''-2.f 3 I 

Ml a 2 <7 3 1 

V^/3 I 



&<# +/ 2 Z C 3 I * * 

c 2 z + tf 2 z a, | * y 
a 2 a: + 7i 2 y & 3 1 — z 



c 2 </ 3 2 + a 3 z I + y 
a 2 7i 3 :r + b 3 y I -r z 



a;' 2 


?/ 2 


Z 2 


yz 


zx 


xy 









n 


8 


5 









6 


12 


9 









7 


4 


To 


7 




-11 




-5' 


-2 


-12 


8 




-3 




-6' 




-10 


9 


-4' 


-1 




4 




-8 


5' 




r 


-9 


5 




8' 


6' 






-7 


6 




9' 


4' 


10 




-5 


2 


-7' 




-6 


11 






3 


-8' 




-4 


12 


-9' 




1 


9' 


-5' 


3 






0' 


1 


7' 


-6' 


0' 






-4' 


2 


8' 




0' 






5 


-3 


8 + 8' 


6 





-1 




6 





9 + 9' 


4 


4 


-2 




5 





7 + 7' 




- 2 


8 


5-5' 





7 


9 




-3 


8 


6-6' 





-1 


7 







9 


4-4' 



Temporary 
Name. 



A 2 

A, 



B 2 

c. 



D 2 



E 2 
E. 



F 2 
F 3 

Oq 

(jr, 



and we find that there are seven of them which do not contain a term in x 2 . Of these, 
however, B 3 , C 3 , D 3 are each derivable from A 2 and A 3 , the connecting equations being 

9A„ - 10 A 2 = OB,, 



6A, 



7 A, = 0C 3 , 



12A 3 - 4A 2 = 0D 3 . 



It is not possible, therefore, to use B 3 , C 3 , D 3 along with A 2 , A 3 in a process of dialytic 
elimination, and we are thus left with only four available equations, viz., A 2 , A 3 , F l5 G r 
On examining whether any pair of the remaining quadrics may be readily used to obtain 
a quadric free of x 2 , we see that the possible pairs are 



Ci , F 3 > C 2 , Gr 2 ; 



E F ■ 

±J 2 ' 2 ' 



E 2 , G 3 ; F , , G- 3 



ELIMINANT OF A SET OF GENERAL TERNARY QUADRICS. 31 

but that because of the relations 

— G 1 + F 3 = G l; 
C 2 + G 2 = F x , 
F 2 - G 3 = C 3 = (6A 3 - 7A 2 ) -=- , 

we are reduced to the use of the pairs E 2 , F 2 and E 2 , Gr 3 , which by addition give the 

quadrics 

. + 7' y 2 + (6-6')z 2 + (0 + 0>z + (9 + 9')zx + 4 xy , 

■ + (7 + 7> 2 + (~6> 2 + (0 + 0')yz + 9 zx + (4-4')oy. 

Further, since the difference of these two is C 3 , i.e., (6A 3 — 7A 2 )-^0, it is immaterial 
which we use along with A 2 , A 3 , F 1? G 2 for the purpose of dialytically eliminating 
y 2 , z 2 , yz, zx, xy. Taking the former of the two, therefore, we have the set 



7V + (6-6> 2 + (0 + 0')yz + (9 + 9>k + 4xy , 

-2y 2 + 8 z 2 + (5-5')yz + zx + Ixy , 

07/ 2 + (-3)z 2 + (8 + 8')yz + 6 zx + Oxy , 

. + z 2 + 7 yz + 4: zx + lOxy , 

Qy 2 + . + 6 yz + 12 zx + 9xy , 



E 2 + F 2 
A, 



from which there results the eliminant 



7 


6-6' 


+ 0' 


9 + 9' 


4 


2 


8 


5-5' 





7 


5 


-3 


8 + 8' 


6 










7 


4 


10 







6 


12 


9 



The extraneous factor contained in it is readily ascertained to be 0, by trying to express 
the determinant as an aggregate of products of complementary minors, one minor of 
each product being formed from the elements of the last two rows, e.g. 



A 10 
12 9 



-01, 



7 10 
6 9 



= -04', 



Of course the cyclical substitution gives two other similar forms of the result. 

(34) When the h's vanish, the ten determinants 

0', 1, 2, 4', 5, 6', 7', 8', 9, 10 
vanish also, and this eliminant of the fifth order degenerates into 



VOL. XL. PART I. (NO. 3). 



6 





9' 


4 


8 


-5' 





7 


3 


8 


6 








7 


4 





E 



32 



DR THOMAS MUIR ON THE 



which by translation of the last row or column to the first place is seen to be axi- 
symmetric. We thus have the following theorem # : — 
The eliminant of the equations 

a x x 2 + \y 2 + c x z 2 + f x yz + g x zx = \ 
a 2 x 2 + \y 2 + c 2 z 2 + f 2 yz + g#x = OV 
a 3 x 2 + b 3 y 2 + c 3 z 2 + f 3 yz + g 3 zx = ) , 

or the expression which equated to zero gives the condition that the loci of 

a x x 2 + b x y 2 + g x x + f x y + c x = 0\ 
a 2 x 2 + b 2 y 2 + g 2 x + f 2 y + c 2 = I 
a 3 x 2 + b 3 y 2 + g 3 x + f 3 y + c 3 = 0) 

have a point in common, is 





1 a A9s 1 


1 «A/ 3 1 


1 a A C 3 


«A#3 1 


1 «l/ 2 03 1 


\a>A c z 1 


1 a iJ2 C 3 


^A/s 1 


1 «A C 3 1 


1 hfrfz 1 


1 Ws 


a A c s I 


1 a iJ2 C 3 1 


1 h°iffs 1 


1 /l C 2#3 



(35) Let us now pass from the eliminants of the fifth order to those of the third. 
Taking the original set of three quadrics, and a derived quadric which is known not 
to be an aggregate of multiples of these, say F 2 of § 33, we have 



a x x 2 + \y 2 + c x z 2 + f x y% + g x zx 
a. 2 x 2 + & 2 2/ 2 + " "< 



+ 



r c 2 z + J $% + g%zx + 
a 3 x 2 + b 3 y 2 + c 3 z 2 + f 3 yz + g 3 zx 
5y2_ S z 2 + (8 + 8') yz + 



h x xy 
h 2 xy 

+ Vw 

6zx + Oxy 



and therefore by elimination of x 2 , y 2 , z 1 



or 

a 2 



c i Av z + 9i zx + K x v 

C 2 fiV Z + 92 ZX + K x v 

c 3 f& z + g$ zx + K x v 

•3 (8 + 8')yz+ 6zx + Oxy 



-3 



A 
A 
A 

! + * 



V z + 



9x 
9 2 
9z 



-3 



zx + 



b a 



-3 



K 



xy = 0. 



Expanding each determinant here in terms of the elements of the last row and their 
complementary minors, we change the equation into 

{0(8+8')+37-56}^ + {06 + 34-512}^ + {00 + 310-59}^ = 0, 

* The result obtained by Lord M'Laren in his paper on " Symmetrical Solution of the Ellipse-Glissette 
Elimination Problem," in the Proc. Roy. Soc. Edin., xxii. pp. 379-387, is the particular case of this where f v f 3 , g 2 , g 3 
are made to vanish and a 1} a 2 , a 3 are put equal to b 2 , b lt b 3 respectively. 



ELIMINANT OF A SET OF GENERAL TERNARY QUADRICS. 



33 



or, since 08' — 56 = —911, into 

(08 + 37 -911>z + (06 + 34-51~2>c + (00 + 310-59)^ = 0. 

From this by cyclical substitution two other equations are obtained, and thence the 

eliminant 

08+ 37-911 06+ 34-512 00 + 310- 59 

00 + lIT- 67 09+ 18-712 04+ 15-610 ( yi ) 

05+ 26-411 00 + 212- 48 07+ 29-810 . 

(36) From the same set of four equations, by the elimination of yz, zx, xy, we find 
in exactly the same way 

{09'-4'6 + l(8 + 8')}x 2 + {-50'-05' + 26 + 7'(8 + 8')}?/ 2 + {30' + 03 + 68'-6'(8 + 8')}z 2 = 0, 
and thence the eliminant 



09'-4'6 + l(8 + 8') 

(0 + 0')l + 49'-4'(9 + 9') 

- 04' + l(5-5') + 9'7 



- 05' + 2(6-6') + 7'8 

07' -51 + 2(9 + 9') 

(0 + 0')2 + 57'-5'(7 + 7') 



(0 + 0')3 + 68'-6'(8 + 8') 

- 06' + 3(4-4') + 8'9 

08'-6'5 + 3(7 + 7') 



(y 2 ) 



(37) The obtaining of a set of three equations in x, y, z may be viewed, of course, 
as the obtaining of a set in x 2 , xy, xz ; or the obtaining of a set in xy, y 2 , zy ; or the 
obtaining of a set in xz, yz, z 2 . Consequently from the set of four equations in x 2 , y 2 , 
z 2 , yz, zx, xy which we have been using a three-fold form of result is possible. 

In the first place by the elimination of y 2 , z 2 , yz and subsequent division by x we 
obtain the equation 

{56 + 37-(8 + 8')0}« + {58' + 32-(8 + 8')5 + 0ll}y + { _53 + 35'-(8 + 8')8 + 6lT}z = 0, 

or, since 56 -08' = 911 and 35 + 88' =611, 

{9lT-37-08}« + {32-58 + 011}?/ + {6lT+35'-88-6ll> = 0, 



and thence the eliminant 



911-37 -08 
412 + 16' -99 -412 
21-47 +0l0 



32-58 +011 
712-18 -09 
510 + 24' -77 -510 



61 1 + 35' -88 -611 
13-69+012 
810-29 -07 



<y») 



In the second place by the elimination of x 2 , z 2 , xz and subsequent division by y we 
obtain the equation 

{-012 + 69-31}a; + { -512 + 60 + 34}?/ + { -(8 + 8')12 + 66 + 39> = 
and thence the eliminant 



-012 +69-31 

-(9_+9')10 + 44 + 17' 
-411 +50 + 26 



-512 +60 + 34 

-010 +47-12 

-(7 + 7')Il + 55 + 28' 



-(8_+8')12 + 66 + 39' 
-610 +40 + 15 

-011 +58-23 



(yd 



34 DR THOMAS MUTR ON THE 

Lastly by the elimination of x 2 , y 2 , xy and subsequent division by z we obtain the 
equation 

{610-04-51}^+ {(8 + 8')l6-07-4'5}?/+ {-310-00 + 59}* = 0, 

and thence the eliminant 



04+ 15-616 07+ 29-810 00 + 310- 59 

00 + 111- 67 05+ 26-411 08+ 37-9IT 

09+ 18-712 00 + 212- 48 06+ 34-512 



(y 5 ) 



(38) Each of these five determinants y x , y. 2 , y 3 , y 4 , y 5 is of the 18th degree in the 
coefficients of the original quadrics, and must, therefore, contain an extraneous factor of 
the 6th degree. It will be seen that the first and last are essentially the same, the 
coefficients of the equations connecting yz, zx, xy being the same as the coefficients of 
one of the sets of equations connecting x, y, z ; that the third and fourth are more com- 
plicated ; and that the second is still more so. 

At the outset the separation of the extraneous factor seemed likely to be a matter of 
considerable difficulty ; a method, however, was fortunately hit upon which effects it 
in every case with comparative ease. This will be fully understood from the following 
application of it to the case of y x or y 5 : — 

Looking at any column of y 5 we observe that the first terms of the three trinomials 
composing the column have a factor in common, that the second terms have also a 
common factor, but that the same cannot be said of the third terms. In the case of the 
first column, for example, the three third terms are —610, —67, —712, where analogy 
would have led us to expect either a 7 in the first term or a 6 in the last. This difficulty, 
however, can be overcome by writing 

either 79 + 04' for 610 
or 46 - 09' for 712 . 

Taking the latter alternative the determinant becomes 

00 +111- 67 05 + 26-411 0(8 + 8')+ 37- 56 

0(9 + 9')+ 18- 64 00 +212- 48 06 + 34-512 

04 + 15-610 0(7 + 7')+ 29- 45 00 +3T0- 59 

and, as a consequence, when we proceed to express it as an aggregate of 27 determinants 
with monomial elements, each of the 27 can have a factor removed from each of its 
columns. Further, when the said factors have been removed, 9 of the 27 must have 
two of their columns alike, and may therefore be neglected. Of the remaining 18 it 
will be found that 3 are symmetrical with respect to the cyclical substitution, and that 
15 can be grouped in triads. The following condensed form of the expansion is thus 
readily obtainable : — 



ELIMINANT OF A SET OF GENERAL TERNARY QUADRICS. 



35 



000 



+ 2012 



+ (123-456) 






5 


8 + 


9 + 9' 





6 


4 


7 + 7' 








5 


9 


8 + 8' 


IT 


6 


6 


8 


12 


7 


II 


6 


4 


8 


12 


10 


5 


9 



+ 2ooi 



- 2015 






6 


8 


7 + 7' 





5 


5 


8 + 8' 


IT 





12 


8 


7 + 7' 


9 


5 


5 


6 


II 



2 004 



+ 2 045 






4 


5 


8 + 8' 





IT 


6 


9 + 9' 


8 





11 


6 


9 + 9' 


8 


12 


4 


5 


9 



Now of the seven complex terms here it is seen that three have 00 for a factor, that is 
a factor of other three, and that in the last does not appear at all. A little investiga- 
tion, however, suffices to show that 00 is a factor of every one. Thus, taking the first 
of the second three, we have 



2012 






5 


9 


8 + 8' 


II 


6 


6 


8 


12 



and similarly 












12 


8 


-2oi5 


7 + 7' 


9 


5 




5 


6 


II 


and 




IT 


6 


2 045 


9 + 9' 


8 


12 




4 


5 


9 



2 012{0(11 12-68) - (8 + 8')(512-89) + 6(56-911)} 

2012{0'03 - (8 + 8+06' + 6-08'}, 
20° 12 (03-6'8-6'8' + 68'): 



- -20015(56'-37-37'-08'), 



20045(34+8'9 + 8'9'-06'), 



The seventh and last, which is the most interesting, may be dealt with in the same way, 
but the resulting identity, viz. 



7 


II 


6 


4 


8 


12 


10 


5 


9 



000', 



is a known theorem regarding compound determinants.* 

* See Mum's " Determinants," p. 216, ex. 7. A more general theorem is obtained thus 
' a x lj 3 1 | \m t f 3 1 I Cl n.J 3 



a ih93 I I h m 293 I I c i>h93 
ajl 2 h 3 1 I bjm^ | | c x nji 3 



= I a lkf3 \{ h m 293 I I Wis I - I h m A I I C l n 293 1} 
" I <h l &3 l{l & l m 2/s I I <V»g&3 I - I \ m i h 3 I I ^2/3 1} 

+ I ajohs \{\ 6 1 m 2 / 3 | | c v n$ 3 \ - \ b^m^ \ \ c x nj 3 |} 
and this expanded form may, by the use of the theorem 

I ^2^3 1 I c i^3 1 = I l x m 2 c 3 1 I 9l n 2 h 3 I + I & 1 m 2 7z 3 1 | c^^ \ + | \m 2 K 3 \ \ c 1 n 2 g 3 \ 



36 



DR THOMAS MUIR ON THE 



Setting the factor 00 aside we consequently obtain the eliminant in the form 



5 

9 + 9' 
4 7 + 7' 



8 + 8' 
6 




+ Zi 






6 


8 


7 + 7' 





5 


5 


8 + 8' 


11 



- 24 






4 


5 


+ 8' 





11 


6 


9 + 9' 


8 



+ 12(03 -6'8-6'8'+ 68') - 15( 56'- 37 -37'- 08') 
+ 45(34 + 8'9 + 8'9' - 06') + (123 - 456)0', 

which, on the development of the determinants, and substitution of 

-±0456 +±049 IT for -±0048', 

-±45512 +±4589 for -±0456', 

±446 IT -±47IIT2 for ±049'II , 

±4678' -±77812 for ±078'9', 

±16711 -±1788' for ±1268, 

±16711 -±1268' for ±17'88', 

±44611 -±1556 for ±4488', 



gives the result of § 31. Denoting, therefore, the eliminant of § 31 by E we have 

7l = 00- E = y 5 . 

In the same way it can be shown that 

y 2 = 0'0'-E, 

y 3 = (2 12 + 6'7)-E, 

y 4 = (-3 10 + 67')-E. 

(39) The extraneous factors in the cases of y 3 and y 4 are in appearance a 
little peculiar, as they give no evidence of being symmetrical with respect to the 
circular substitution. That they really possess this symmetry is, however, readily 



be changed into 



and thus into 



I a ihf 3 



{| \m 2 c. 
{I h m 2 C i 
{l \™*h 



IffiV^I + I W m 2>h\ I C l92 J h\} 
if 1 n 2 h 3 \ + | b 1 m li n 3 \ | cj 2 h 3 \} 
I f x n 2 g 3 1 + | bjm.fig | ! Cl f 2 g 3 | } 



I bjm 2 c 3 | • {I a x l 2 f 3 1 ! g 1 7t^ z 
+ I b 1 m 2 n 3 \ ■ {| a x l 2 f 3 | | Cl g 2 h 3 

so that by a second use of the said theorem we have 



and finally 



or by a third use of the same theorem 



- I 6,m 2 c 3 
+ | b l m. i n 3 

\fi9zh\ 



I ftfjh 



I a ih9 s I ( AnJh 
I a ik9z 1 I cJJh I 

I a ih n 3 I I fi9ih I 
I «A C 3 I I fi9A I 



+ I «i^3 



I J \n>29 3 1 } 



6 1 m 2 w 3 1 
b x m 2 c 3 1 



a x l 2 n 3 

ft 1^2 C 3 



I b{m.,a 3 1 I c x n 2 a 3 



ELIMINANT OF A SET OF GENERAL TERNARY QUADRICS. 37 

established by obtaining for them equivalent expressions which bear the symmetry 
on their faces. 

Of such expressions three at least are useful in the process of separating E from its 
co-factor. These are, in the case of y 3 , 



K±lTT + ±4'8), 1Q111 ^- 789 , 12 3 + 4W . 

The first arises from the theorem repeatedly used in the note to § 36, — a theorem which 
ensures the identity of 

2 12 + 67, 3 TO + 4'8, 1 TT + 5'9 , 
and therefore gives 

2 12 + 67 = K2lll + 24'8). 

The second and third have essentially the same source, for from it we obtain 

02l2 + 067 - (10 TT-57)T2 + (5 T2-89)7 , 

= TO TT T2 - 7 8 9 ; 

and 

0'212 + 0'67 = 2(13 + 6'9') + 6'(4'5'-29') , 

= 12 3 + 4'5'6' . 

The similar expressions for the extraneous factor 67' — 310, which occurs in the case 

of y 4 , are 

t^-iTT *aq'\ 10TTT2-4 5 6 12 3-7'8'9' 
^2,lll-Z4»;, q , - t ; 

and it may be noted in passing that there is a third triad of such equivalent expressions, 
viz. 

K±4'8 + ±48% 456 ~ 789 , 4W + 7W 

which are got from the two previous triads by subtraction. 

(40) To each of these triads, however, a fourth member may be added, as there exist 
symmetrical expressions of a quite different kind which can be proved equal to 
2 12 + 6'7, 67'- 3 10, 67 + 59' respectively. 

The origin of this is an identity in compound determinants, viz. 



7i£> I 7 2 & I I 7s£i 



"l^S I i «1^2^3 II II Ptfda I I /3l*7 2 73 

Ti&fs I I 7i&Aj I I I I «i^2?3 I I ai&73 

I I 7i&£$ I I 7i&«3 

I I fefs I I A^s 



38 DR MUIR ON THE ELIMINANT OF A SET OF GENERAL TERNARY QUADRICS. 

the first part of which is established by multiplying the determinant on the left by 
| T73& I in the form 

Vi P s • 

>h Pi ■ 

>/2 & 1 

and then removing the same factor from the product; and the others by making a 
cyclical change in the rows of the original determinant and using the part already 
proved. 

Thus, putting a, & y, £ , h J=a, b, c,f, g, h, we have 
I I «i/ 2 I I « 2 / 3 i I a Ji 

I h i9* I I \g A I I \y x 



C A 



c 2 h 3 



cj h 



= 59' + 67 = 67' + 4'8 = 48' + 5'9 ; 
putting a, ft y, £ v , £=a, b, c, g, h,f, we have 

= 111 -48' = 212-59' = 310-67'; 
and putting a, ft y, £ v , f = a, 6, c, ft, /, #, we have 

= 4'8 + 3 10 = 5'9 + 1 IT - 6'7 + 2 12 . 



a i92 I I a oJ S I I «3#1 
& A I I 6 2^3 I I h h l 
C l/ 2 I I C 2 / 3 I I c zfi 



a 2^3 I I a 3^1 



a 1 A 2 

& i/ 2 I I ^2/3 I I 63/1 
°i9% I I H9% I I H9x 



What is still more interesting is the fact that, when £ 77, £ are made equal to ft y, a, 
the above theorem in compound determinants degenerates into the theorem regarding 
the adjugate ; and that we thus obtain 



a A I I a $z I I a A 



¥2 

c x a 2 



& 2 C 3 



h c l 



= 00, and 



I flffs I I / 2 #3 I I fsffi I 

i 9 A I I # A I I 9 A I 



= 0'0' 



The diversity in the extraneous factors is thus seen to disappear entirely, the results 
being 



y, = I 



aJ) a 



b 9 c 



2^3 



3«l I I • E = y 5 , 



y-2 = I \fi92 1 1 Ms 1 1 Vi 1 l ,E ' 

73 = -| |«AI I \A I I «tfl I l-E, 
V4 = -| fl^ 8 1 \b 2 h s I J oj/j I |-E. 



( 39 ) 



IV. — On the Convection of Heat by Air Currents. By Prof. A. Crichton Mitchell. 

(With a Plate.) 

(Read March 6, 1899, and December 18, 1899.) 

1. The present paper deals with a series of experiments made in the Physical 
Laboratory, Edinburgh University, from January to October 1899, with the object of 
determining the convective loss of heat from a cooling body owing to the action of 
currents of air. 

2. As some of the results obtained have a bearing on the history of the laws of 
cooling, it is necessary to refer to at least one of the investigations which have been 
made on the subject. The first to give any definite statement regarding the law of 
cooling was Newton. In a paper # communicated to the Koyal Society of London, his 
experiments on cooling are detailed, and his conclusion stated as follows : — 

" Nam color quern ferrum calefactum corporibus frigidis sibi contiguis dato tem- 
pore communicat, hoc est Color, quern ferrum dato tempore amittit, est ut Color totus 
/em, 

Since this appeared in 1701 it has been known as Newton's Law of Cooling, and has 
generally been reproduced in some such form as " The rate of cooling of a body at any 
temperature is proportional to the difference between that temperature and the tempera- 
ture of the surroundings of the body." Or more shortly, "Rate of cooling is propor- 
tional to temperature excess." 

But at the end of his paper Newton makes the following important statement : — 

" Locavi autem ferrum non in cere tranquillo, sed in vento uniformiter spirante, 
ut cer a ferro calefoctus semper obriperetur a vento, et cer frigidus in locum ejus 
uniformi cum motu succederet. . . . Sic enim ceris portes cequoles cequalibus tem- 
poribus calefoctus sunt, et calorem conceperunt calori ferri proportionalem ." 

Strangely enough, nearly all subsequent references to Newton's Law of Cooling omit 
any mention of its most important qualification, viz., that the cooling body is placed in 
a current of air moving with uniform speed. The only clear exception is Fourier's 
remarks on Newton's Law in § xxxi. of his paper,t " Questions sur la theorie physique 
de la Chaleur rayonnante," where he points out that the cooling of bodies in still air, or 
rather in air which has no other movement than that resulting from change in density, 

* "Scala graduum caloris et frigoris," Phil. Trans., April 1701, vol. xxii. p. 824. Also in Newton's Works, 
Horsley's edition, 1782, vol. iv. 

t Ann. de Cli. et de Physique, 1817, vi. pp. 259-303. 

VOL. XL. PART I. (NO. 4). F 



40 PROFESSOR A. CRICHTON MITCHELL ON THE 

follows a different law which Newton has not taken into consideration. That Fourier 
correctly appreciated the importance of the condition attached to Newton's Law of 
Cooling, viz., that the body was placed " non in sere tranquillo, sed in vento uniformiter 
spirante," is seen from the exceedingly careful manner in which he defined # the 
coefficient h, the ' conductibilite exterieure ' of a body. 

But the long succession of commentators, from Martine onwards, have practically 
criticised Newton's Law on the assumption that the cooling body was placed in 
(so-called) still air. Dulong and Petit only refer to its most important condition as 
the action of a constant cooling cause. 

So far as I am aware, Leslie t was the only one who attempted to realise experi- 
mentally the conditions required in any investigation whose object is to determine the 
accuracy or otherwise of Newton's Law of Cooling. A metallic vessel, containing water 
at a temperature above that of the air, was tied to the end of a string and whirled in a 
circle for a definite period of time, after which the diminution in temperature of the 
water was noted. From an experimental method of this kind, little could be expected 
by way of accurate result. 

3. In nearly all the experiments (excepting those of Leslie referred to above) 
hitherto made to determine the law of cooling, the cooling body has been placed either 
in (so-called) still or free air, or in a vessel containing air whose pressure is different 
from that of the atmosphere, or in a (so-called) vacuum. It has always appeared to me 
that experiments of the kind must lead to results of a doubtful type, owing to the 
indefinite character of the conditions under which they are made. The shape of the 
cooling body must undoubtedly affect the direction, as the size will affect the speed, of 
the currents of air by means of which convection is carried on ; } and, as a consequence, 
experiments made with cooling bodies of different shapes and sizes are not comparable 
so far as the determination of emissivity is concerned. The unsteadiness of so-called 
still air must also affect the results, for, as will be shown later in this paper, currents of 
air of speed so low as to make them almost imperceptible to the unaided senses, are 
sufficient to exercise an appreciable effect on the rate of cooling of a body. It would, 
in short, appear as if a carefully-defined unit of ' convectivity ' (to coin a word for con- 
vection analogous to that for conduction) were required. 

4. The method adopted in the present inquiry consisted in exposing a heated body 
to the cooling action of currents of air of different speeds, determining the temperature 
of the body at successive intervals of time, and thereby estimating the rate of cooling 
at given excesses of temperature at different speeds of the air current. 

The apparatus employed is represented in fig. 5, and consisted essentially of the 

* Tlieorit Analytique de la Ckalew, eh. i. sect. ii. 

t Leslie, An Experimental Enquiry into the Nature and Propagation of Heat, London, 1804, p. 279. 

X See Porter. Phil. May., xxxix. 268-279. 



CONVECTION OF HEAT BY AIR CURRENTS. 41 

following parts : — (1) The heated body; (2) arrangements for producing a current of 
air whose speed could be varied ; (3) an instrument for registering the speed of the air 
current ; (4) means for determination of the temperature of the body from time to 
time. 

The body experimented upon was a copper ball, 2 inches in diameter. A circular 
hole, f inch in diameter and 1^ inch in depth, was bored radially so as to admit a 
thermo-electric junction. Opposite to this hole a copper hook was screwed into the ball, 
by which means the ball was suspended. Previous to each experiment the surface of 
the ball was cleaned, and then carefully blackened by exposing it to the sooty flame of 
a turpentine lamp. Care was taken to blacken the ball as nearly as possible in the 
same way for each experiment.* It was then heated in one of Fletcher's circular gas 
furnaces ; a piece of fine wire gauze being placed between the ball and the flame from 
the air-gas jet, to prevent the flame either burning or blowing off the lampblack 
deposited on the surface (see fig. 1 in section and fig. 2 in plan). During the process 
of heating, the wire suspending the ball was twisted so as to make the ball rotate 
rapidly about its vertical diameter, in order to prevent any one side of the ball being 
heated more highly than another. For each experiment, the ball was heated for the 
same time, viz., fifteen minutes, and when taken out of the gas furnace its temperature 
was approximately 400° Centigrade. 

The arrangements for producing a steady current of air consisted of one of the 
Blackman Ventilating Company's fans (fig. 5, E), 32 inches diameter, fitted into a 
triangular frame, GF, in the side of an air-tight wooden box, A B C D, whose dimensions 
were 5 feet in length, 6 feet in breadth, and 6 feet in height. The fan had a pulley, H, 
on its outer side, and by means of a belt passing over this to a shafting driven by a gas 
engine the fan was made to revolve at a sufficiently high speed, and thereby exhaust 
the air in the box. Into a circular hole in the box, on the side opposite to that holding 
the fan, one end of a tinned iron tube, KL, 5 feet long and 6 inches in diameter, was 
fitted. When the fan revolved air was drawn into the box through the tube. The 
speed of the fan was the same for all the experiments, but in order to obtain different 
speeds of air through the tube a movable, slit (fig. 3 longitudinal section, fig. 4 trans- 
verse section) was placed at the end of the tube where it entered the box ; and by 
widening or narrowing the slit the speed of the air current could be increased or 
decreased between the limits of 10 and 1000 metres per minute. 

It was necessary to obtain a current the stream lines in which were parallel to the 
axis of the tube. That such was obtained was proved by allowing smoke (tobacco 
smoke or sal-ammoniac fumes) to be drawn into the tube at L when the fan was 
working, and noticing the direction taken by it in passing through the tube. The 
necessity for such a precaution was noticed during some preliminary experiments made 
with a fan of 12 inches diameter fitted to the wider end of a conical tube. The 

* It is very desirable that some coating be found, similar to that of soot or lampblack, which will not readily rub 
off, or be affected by steam or exposure to a high temperature. 



42 PROFESSOR A. CRICHTON MITCHELL ON THE 

diameter of this tube at the wider end was the same as that of the fan, and at its 
narrower end 6 inches. But this small fan had been so constructed that it could only 
drive air into the tube. I found that when this was done the air driven through the 
tube had no steady motion ; that, in fact, its path resembled a spiral. 

The large wooden box into which the 30-inch fan was fitted was necessary for two 
reasons. First, in order to get the most work out of such a fan for a given rate of 
revolution it is necessary that it be allowed (what is termed by ventilating engineers) 
'free feed' and 'free discharge.' In other words, it must catch up air from a free 
space, and must discharge it into a free space. The wooden box fulfilled these condi- 
tions sufficiently for all practical purposes. Second, the box acted as a regulator of the 
speed of the air current through the tube when this might tend to vary owing to an}^ 
slight irregularity of the gas engine which drove the fan. 

The end of the tube farthest from the fan was surrounded for a distance of 1^ feet 
by a water jacket, M, into which water from a cistern entered at Q, and was discharged 
a,t P. The temperature of the water entering the jacket was, in all the experiments, 
nearly that of the air passing through the tubes. In any case where the temperatures 
of air and water differed by more than 1° Centigrade the results of the experiments were 
not employed in the final deduction of results. 

The copper ball, after being heated, was so suspended by its hook from a loop of 
copper wire fastened to the inner surface of the tube that its centre was in the axis of 
the tube, and in the middle section, P, of the jacketed portion of the tube. 

The instrument employed to determine the speed of the current of air was an 
aluminium fan anemometer, constructed by Richard Freres of Paris. It was placed in 
the position N shown in fig. 5, and so rested on three guides that its centre was in the 
axis of the tube. It was found that with a given speed of the fan, the speed recorded 
when the ball was hanging in the tube was lower than when the ball was not in the 
tube. This difference, which was due to the ball disturbing the steady motion 
of the air through the tube, was greater at higher speeds. Allowance was made 
for it by directly observing its amount for each speed at which an experiment was 
made. 

The temperature of the copper ball was' ascertained by means of a thermo-electric 
junction of iron and German silver, which passed through a pumice-stone plug placed in 
the circular hole bored in the ball. The junction of the two wires forming the circuit 
was as nearly as possible at the centre of the ball. A Thomson's reflecting galvanometer 
was included in the circuit. The value of unit deflection on the scale was ascertained 
after each experiment by noting the deflection produced by placing the junction in 
steam issuing from boiling water, and also noting the temperature of the mercury pool, 
which formed the cold junction of the circuit. 

During the process of cooling, readings of the deflections on the galvanometer scale 
were taken from time to time. As a rule, unit deflection on the scale represented a differ- 
ence in temperature of 2° Centigrade. The error in reading the scale did not likely 



CONVECTION OF HEAT BY AIR CURRENTS. 43 

exceed one-tenth of a division, that is, 0°*2 Centigrade. The interval of time between 
any two readings was generally chosen, so that the corresponding decrease in deflection 
was not less than ten divisions. The error in any one estimate of the rate of cooling 
during a given interval would therefore not exceed 1 per cent. 

5. Fourier's equation for the motion of heat in a solid homogeneous sphere is 

dv _ K /d 2 v 2 dv\ 
& ~ GT> \dr* + rdr) 

with the condition that at the surface (r = R) 

tt- dv 

K -j- + hv = 
dr 

The solution for t = must, of course, be satisfied by the function of v and r represent- 
ing the initial distribution. The solution for the particular case of uniform initial 
distribution is 



2 



er K 



2/>R \1 sm R- 



' ; = K~ /i -*- 



— ( iY 

CD \r) t 



<;cosece — cose 
R 



where e 1} e 2 , etc., are the roots of the equation 



!E -1-i-B. 



tan e R K 

After some time has elapsed, the first term in the series for v is the only one of 

practical value. Further, if R be small, or the ratio r^ be small, the temperature 

throughout the sphere will be uniform. To test this, we may take Macfarlane's determi- 
nation # of the emissivity of a black surface and the value of K (thermal, not thermo- 
metric, conductivity) for copper to be 0*95 in C.G.S. units. With these assumptions it 
will be found that the difference between the temperature for r = and r = 1 when 
t = 600 is within the limits of experimental error. It may, therefore, be assumed that 
the temperature at the centre of the ball is that of the ball generally. 

6. The experimental results obtained may be regarded in two ways. First, their 
bearing on the law of cooling, stated by Newton ; second, the rate of cooling for a 
given excess of temperature with different speeds of the current of air. 

As regards the first of these, Newton gives no details as to the speed of the current 
-of air in which he placed the cooling body, and merely states that it was placed " in 

* Proc. Roy. Soc, xxxii. 465. 



44 



PROFESSOR A. CRICHTON MITCHELL ON THE 



vento uniformiter spirante." It is unlikely that the air current was produced arti- 
ficially ; most probably it was simply a breeze of wind which Newton believed to be 
blowing with uniform speed. Let us assume its speed to have been about eight miles 
per hour, and examine the results of an experiment made on the copper ball at or near 
that speed. The following table gives the rates of cooling in a current of air whose 
speed was 271 metres per minute (8 "09 miles per hour) : — 



Rates of cooling (degrees 
Centigrade per minute). 



40 



Temperature Excess. 
80 120 160 



200 



39 



8-0 



12-0 



16-2 



20-6 



From these figures it follows that the rate of cooling in a current of air whose speed 
is 217 metres per minute is proportional to the temperature excess, up to at least 120° 
of temperature excess, beyond which it proceeds according to some law involving terms 
higher than those of simple proportion. 

Let us now take an experiment at a higher speed. At 1031 metres per minute the 
rates of cooling were as shown below : — 



Rates of cooling (degrees 
Centigrade per minute). 



40 



Temperature Excess. 
80 120 160 



8-9 



17-8 



26-7 



35-6 



200 



44-5 



Hence the rate of cooling at the higher speed of 1031 metres per minute is pro- 
portional to temperature excess up to at least the higher temperature excess of 200°. 
Other experiments confirm this result, and justify the following general statement — at 
least within the limits of 200° temperature excess, and an air-current speed of 1000 
metres per minute : — 

When a heated body is placed in a current of air of uniform speed the rate of 
cooling is proportional to the temperature excess, up to a temperature excess which 
increases with increasing speed of the current of air. 

Another way — and from a historical point of view the more interesting way — of 
stating the result is, that 

Newton's Law of Cooling is accurate under the conditions premised by him, 
provided the speed of the current of air passing the surface of the cooling body be 
sufficient. 

It is necessary that this result should if possible be explained. I do not, of course, 
mean that the Law of Cooling generally is represented as above. Cooling is not the 



CONVECTION OF HEAT BY AIR CURRENTS. '45 

result of one action, but of at least three — radiation, convection, and conduction. 
Leaving the last out of consideration meanwhile, the law of radiation is known to 
involve higher powers of the temperature excess than the first. The amount of heat 
carried off by convection may be assumed to be proportional to temperature excess. 
Consequently, if the amount of heat radiated during unit time at a given temperature 
excess remain constant and comparatively small, while the amount lost by convection 
be considerably increased, the total rate of cooling due to both causes will become more 
nearly proportional to temperature excess. A rough estimate, deduced from results 
given later on, may be made of the relative amounts of heat lost by radiation and 
convection. When the copper ball was exposed to an air current of a speed of 1000 
metres per minute, the rate of cooling, at a temperature excess of 50°, was 2|-° per 
minute due to radiation, and 7° per minute due to convection. 

This seems to me an explanation of the result quoted above. 

I would suggest that Fokbes' method of determining thermal conductivity might be 
improved by the application of the above result. The bar experimented upon might 
serve for both parts — statical and cooling — of the experiment, and in both it might be 
exposed to a current of air passing across its breadth. The amount of heat lost by 
cooling during the statical experiment might then be determined with greater exactness 
than in the usual way. 

7. As regards the rate of cooling at a given excess of temperature with different 
speeds of the cooling current of air, the results obtained are given in tabular form in the 
Appendix to this paper, Considering the many minute points in regard to which the 
experimental conditions might vary, the results are fairly concordant. 

For a temperature excess of 50° the rates of cooling at different speeds of the air 
current were plotted as ordinates in a curve, the abscissas in which were the different 
speeds. For 80° and 100° the same was done. The curves are shown in fig. 6. 

A glance at these curves will show that the rate of cooling at a given temperature 
excess increases with the speed ; at first almost proportionally to the speed, but after- 
wards more slowly. With regard to this peculiarity I would offer the following remarks 
by way of possible explanation. 

Were the copper ball exposed to an air current whose speed gradually increased, 
there will obviously be reached a speed at which the motion of the air will cease to be 
steady motion ; vortices will be formed, or the motion will become turbulent. It is 
reasonable to suppose that, until this speed is reached, the rate of cooling at a given 
excess will be proportional to speed. Beyond that speed, there being less and less 
steady motion of air past the surface of the ball, the cooling effect of the current will 
be less than proportional to its increase in speed. In this way the change in curvature 
of the curve might be explained. I attempted to determine the speed at which the 
motion of the air ceases to be steady, by allowing sal-ammoniac fumes to be drawn into the 
tube, gradually increasing the speed of the air current, and observing the direction taken by 



4G PROFESSOR A. CRICHTON MITCHELL ON THE 

the stream lines of fumes in passing round the ball. The results were, however, indecisive. 
Perhaps a better indication as to whether such a critical speed really existed is afforded 
in another way. I have already stated that the speed recorded by the anemometer 
when the ball was hanging in the tube was less than when the ball was not in the tube, 
and that this difference varied with the speed. If now a curve be drawn whose ordinates 
represent this difference, and whose abscissae represent the speeds with the ball in the 
tube, it will be seen that when a speed of about 450 metres per minute is reached the 
ordinates begin to increase much more quickly. This may be due to the motion of the 
air in passing, and after having passed, the ball ceasing to be steady at this speed, and 
therefore recording less in the anemometer. If, now, the curves in fig. 6 be examined, 
it will be seen that up to about the same speed the rate of cooling is nearly proportional 
to speed, but beyond that it is less than proportional to speed. I am therefore inclined 
to think that the change in curvature in the curves of fig. 6 is due to the motion of the 
air ceasing to be steady at or about a speed of 450 metres per minute. 

Of course it is to be remembered that these results apply only to a cooling body of 
the shape and size of that used in this investigation. Were either shape or size 
different, the results would be different. 

An improved method of experiment would be to heat a strip of platinum foil by 
means of an electric current, allow it to cool while exposed to a current of air passing 
across its breadth, and ascertain its temperature from time to time by means of its 
electrical resistance. It would then be possible to determine in absolute measure the 
amount of heat lost in unit time from unit surface for different excesses of temperature 
and for different speeds of air. No question regarding the character of the motion, 
steady or otherwise, of the air would then be involved. 

There is another aspect of the question which deserves consideration. If the speed 
of the air current were increased enormously, friction between the air and the ball 
would generate heat, and thereby lessen the rate of cooling. That such would be the 
case is known from the behaviour of meteors in passing through the earth's atmosphere. 
Now, if the friction between highly rarefied air and a meteoric body moving at, say, 
20 miles per second, is sufficient to render the body incandescent, the amount of heat 
similarly generated in air at the earth's surface with a speed of 45 miles per hour (a 
speed attained easily by the apparatus employed) may be sufficiently large to be 
measurable by experimental means. 1 tried to detect any result of this kind by the 
following experiment. The ball was placed in the tube, and allowed to remain there 
for forty-eight hours, so that its temperature might become the same as that of its 
surroundings and of the air in the room.* A Boys' radio -micrometer was fitted up in 
such a position that any rise in temperature of the surface of the ball might be at once 
detected. A current of air with a speed of about 45 miles per hour was then allowed 
to pass along the tube for ten minutes, after which the screen between the ball and 

* The experiments described in this paper were conducted in an underground cellar, in which the diurnal variation 
of temperature is scarcely noticeable. 



CONVECTION OF HEAT BY AIR CURRENTS. 



47 



radio-micrometer was removed. Unfortunately, the circuit of the radio-micrometer was 
so delicately suspended that the vibration of the flooring, owing to the working of the 
gas engine, caused the spot of light on the scale to oscillate irregularly. I am not 
prepared to say whether the deflections observed were or were not partially due to a 
heating of the ball by the current of air. The time at my disposal, being furlough from 
India, did not allow of further inquiry in this direction. 

I have to acknowledge with many thanks Professor Tait's kindness in allowing me 
to make use of his laboratory and to draw upon its resources for the purpose of this 
investigation, and for otherwise assisting me with advice regarding it. I am also 
indebted to my friend Mr Robert Dickinson for some of the drawings published along 
with this paper. The Edinburgh University Court sanctioned a grant from the Moray 
Bequest for the purchase of apparatus required for the work. 



APPENDIX. 

Bates of Cooling {Degrees Centigrade per Minute) at different Temperature Excesses and for different 

Speeds of the Air Current. 



No. of 
Experiment, 


37 


2 


9 


11 


12 


27 


28 


17 


19 


18 


21 


29 


25 


26 


Speed of 
Air Current, 


41 


79 


133 


149 


187 


240 


301 


388 


436 


497 


597 


643 


758 


976 


10 


0-47 


0-58 


0-72 


0-71 


0-90 


0-97 


107 


1-20 


1-18 


1-34 


1-37 


1-44 


1-35 


1-80 


20 


0-94 


1-16 


1-44 


1-45 


1-76 


1-83 


2 00 


237 


2-42 


2-82 


2-91 


2-99 


2-87 


362 


30 


1-43 


1-76 


218 


2 23 


2-67 


2-83 


3-11 


351 


3-76 


4-23 


4-45 


4-57 


4-97 


5-40 


40 


193 


2-37 


2-91 


3'04 


353 


3-81 


4-18 


4-71 


515 


5 63 


6-00 


621 


6-69 


7 34 


50 


238 


2-98 


3-68 


3-81 


4-43 


473 


5-20 


602 


6-45 


7-05 


7-63 


7-77 


8-44 


921 


60 


2'98 


359 


4-39 


4-65 


5-29 


5-66 


6-06 


7-29 


7-90 


8-50 


9-21 


934 


10-27 


11-10 


70 


3-58 


4-19 


5-15 


5-44 


6-19 


6-64 


737 


8-65 


931 


9-94 


10-83 


11-07 


11-98 


1295 


80 


4-09 


4-79 


5-89 


6-19 


7-14 


7-63 


8-44 


9-99 


1072 


11-37 


12-24 


12-66 


13-75 


14-77 


90 


4-64 


5-39 


683 


7-01 


7-98 


8-65 


9-56 


11-30 


12-14 


12-86 


14-02 


14-20 


15-68 


1667 


100 


5-22 


5-99 


7-77 


7-91 


8-86 


972 


1069 


12-55 


13-61 


1433 


15-55 


15-81 


17-47 


18-67 



VOL. XL. PART I. (NO. 4). 



Trans. Roy. Soc. Edin. 

Dr. Crichton Mitchell on the Convection of Heat by Air Currents. 



Vol. XL. 



Fig. 5. 




'. ■ ■ ■ • • - • ~~ 




Fi S 4 Fid 3. 



i^X 



V£ 




\\D 



o 
o 
U 
u. 
O 

w 




200 



4-00 600 

Speed of Air Current (metres per minute). 



800 



IOOO 



■A # ^ 



( 49 ) 



V. — A Development of a Pfaffian having a Vacant Minor. 
By Thomas Muir, LL.D. 



(Read March 19, 1900.) 



(l) The simplest possible case of the development referred to in the title is one 
which is seen to follow instantly from the determinant definition of a Pfaffian. Thus, 
by the said definition, 



1 


• • a 4 


«5 


a 6 


-J 










a 4 


a o «6 






• \ 


h 


h 






h 


h h 






C 4 


C 5 


°6 






c 4 


H C 6 








d 5 






- «4 - h 


-''4 


d o d 6 

■ e 6 




and therefore 


• 








- «v, - h 


~ % ~ <h, 


- e 6 • 


) 










= v/{- 


a 4 a 5 
b, b. 

4 D 


a G 




- a i 

~ C 4 


- a- - a G 

- b. - b r 

- C r - C a 

b o 










= J\ a i h c e ! 2 . 














= ± 


a i 


h 5 C 6 1- 













the result reached being that a Pfaffian with certain zero elements is expressible as a 
determinant. It should be noted that, as in many instances where this form of defini- 
tion is used, there is an ambiguity as to sign : it is of less importance to note that here 
the appropriate sign is — . 

(2) Another case may readily be established by using either as a definition or as a 
proved theorem the recurrent law of formation which, in the original notation of Jacobi 
and Cayley, is exemplified by the identity 

[123456] = 12[3456] - 13[2456] + 14[2356] 

- 15[2346] + 16[2345]. 

Thus when there is onlv one zero element and the Pfaffian is of the 3rd order, we have 



a,, 



a b 


«6 


= * 6 \ 




a 3 


a 4 


h 


h 






h 


h 


C 5 


C 6 








c i 


d, 


e 6 


+ c e| 




«4 
&4 


a 5 






+ %\ 


h 




h 

d. 



- d R 



- b R \ a Q 






VOL. XL. PART I. (NO. 5). 



H 



50 DR THOMAS MUIR ON 

But, by the previous case, the 1st, 2nd, and 3rd terms of this expansion are equal to 



e |a 3 Z> 4 l , + tfelog&sl , - c G \aJ) b \ 



respectively ; and the remainder 



= - | a A a A a A 



+ I a 6 b 3 a fi & 4 a 6 b 5 



C. Cc 



= | «6 & 3-«3 & ti «6 6 4~ a A % b b~ a A 



d< 



= ~ hMh + \ a Ah ~ l a Ai c 4 



Consequently we have the result 



a, a. a, a R 



\ 


h 


h 


h 




C 4 


C 5 


C G 






d 5 


d 6 



- I«3 & 4l e 6 + \ a 'A\ d 6 ~ \ a A\ C 6 

- \a 3 b G \d 5 + \aJ) Q \c 5 - \a b b 6 \c v 



where the first factors on the right are the set of six (C 4i2 ) two-lined determinants 
formable from 

«3 a i a 5 «G 
h b 4 h b 6> 

and their cofactors are the remaining six (3 + 2 + 1) elements 

*A Cr Co 



d 5 d 6 



of the Pfaffian. 



(3) Had the given Pfaffian been of a higher order than the 3rd. it is clear that the 
cofactors of the two-lined determinants could not have been linear. It will now be seen 
by considering another case that in general they are themselves Pfaffians, and that con- 
sequently in the case just dealt with they have in strictness to be viewed not as elements 
but as Pfaffian minors of the 1st order. The expansion to which we are leading may 
thus be described as an aggregate of terms each of which is a product of a determinant 
and a Pfaffian. 

As before we have 



«3 


«4 


«5 


H 


a 7 


a s 


\ 


h 


h 


\ 


h 


\ 




C 4 


C 5 


C 6 


c 7 


e s 






d* 


d 6 


dj 


d s 








e e 




ft 

9s 



A DEVELOPMENT OF A PFAFFIAN HAVING A VACANT MINOR. 



51 



= 9%\ 



a 3 a 4 a 5 a 6 

b 3 Z> 4 % b G 

c i c 5 c 6 

d 5 d 6 



A 



a 3 a 4 a 5 a~ 

h h h b r 



d 5 d r 



+ c s 



a, a K a R a 7 



d 6 d 7 



A 



ft 8 j a 3 a 4 



a 5 


«6 


a 7 


C 5 


C 6 


C 7 


<*5 


^6 


rf 7 




e 6 


e 7 

A 



a 8 l 6 3 5 4 



*5 


*6 


6 7 


C 5 


C 6 


C 7 


^5 


^6 


^7 




e 6 


e 7 
A 



where, again, all the terms on the right except the last two can be dealt with by using 
the preceding case, the result of such use being an expression consisting of 30 {i.e., 5x6) 
terms of the form 

On examination, however, it will be found that these can be grouped in sets of three 
by reason of the fact that each of the ten (i.e., C 5j2 ) two-lined determinants appearing in 
the expression occurs three times. For example, the determinant | a 3 6 4 1 occurs the first 
time, as we have just seen, with the cofactor —g%e 6 , the second time withf s e 7 , and the 
third time with —e & / 7 ; its full cofactor thus being 



(^6-/s e 7 + e s/7) 01 ' 



- e.. e* e Q 



A /■ 



ffs 



By condensation in this way, therefore, there is obtained from the first five terms of the 
development with which we started an expression consisting of ten terms of the form 



- J a._ i b i J • J e e e 7 e s 

A A 

9 S 



As for the remaining two terms of the said development, the same reasoning as before 
gives their aggregate 



= j a sh- a A «8 5 4-«A a S h 5~ a 5 b S a $h- a 6 b S «8 & 7 " V's 



t 7 
A 



= ~ I a S h 8 I • I d 5 d 6 d 7 

e 6 e 7 

A 



+ I a 4 6 8 J . J c 5 c 6 c 7 
e 6 e 7 

A 



a A I • I C 4 C 5 C 6 



d 5 d 6 



52 



DR THOMAS MUIR ON 



We thus have as a final result 



<*6 


a 7 


a s 


= ~ | «2 & 4 | • 


I e 6 


e 7 e s 


^6 


h 


h 






fl /s 


C 6 


c 7 


c s 






9s 


** 


d 7 


d s 








e 6 


e 7 

A 


e s 
/s 
<7s 









- I a-l* i 



"4 °5 °6 



where the first factors of the terms on the right are the fifteen (i.e., C 6i2 ) two-lined 
determinants forma ble from 



a s a 4 a 5 a G ct 7 cc s 
\ ^4 h & <i h h 



and their cofactors are the fifteen (i.e., 5 + 4 + 3 + 2 + 1) principal minors of the Pfaffian 



C 5 


C (3 


C 7 


c s 


h 


d. 


d 7 


d s 




e 6 


e 7 


e s 






A 


fs 
9s 



the first determinant | a 3 6 4 [ going along with the complementary minor of the first 
element c 4 of the Pfaffian, the second determinant | a 3 b 5 | going along with the comple- 
mentary minor of the second element c 5 of the Pfaifian, and so on in every case. 

(4) For the full investigation of the general theorem thus shadowed forth, neither 
of the definitions here employed is well suited : what is needed is a definition prescrib- 
ing the mode of formation of the terms from the elements and the mode of determining 
the sign of each term — a definition, that is to say, similar to that ordinarily used for a 
determinant. The following will be found to satisfy these requirements : — 

If n(2n— 1) elements be each numbered by a 'pair of integers in order of magni- 
tude, and be arranged in semiquadrate form, thus — 



12 13 14 
23 24 



l,2n 

2,2n 



2n-l,2n 

and all possible terms be taken which are products of n elements whose united place- 
numbers include all the integers from 1 to 2n, the sign of each term being taken + or 
— according as the number of inverted-pairs in the series of integers specifying the 
term is even or odd ; then, the function which is the aggregate of these terms is called 
a Pfaffian of the n th order, and is denoted by the semiquadrate collection of elements 
bounded by two straight lines, a shorter on the left and a longer on the right. 



A DEVELOPMENT OF A PFAFFIAN HAVING A VACANT MINOR. 



53 



For example, the Pfaffian of the 2nd order, 



12 13 14 

23 24 

34 



= 12.34 - 13.24 + 14.23 



(5) Instead of the elements being viewed as forming 2n— 1 rows of 2n — 1, 
2n — 2, . . . , 1 elements respectively, and at the same time 2?i— 1 columns of 1, 
2, . . . , 2n— 1 elements respectively, they may, without alteration of position, 
be viewed as situated at the intersections of 2n frame-lines each containing 2ft — 1 
elements, the r th frame-line being in every case made up of the r th row and the 
(r— l) th column: and from this point of view the two integers used to specify 
an element are the numbers of the two frame-lines in which the latter is situated. 
This will be apparent from a glance at the following diagram of frame-lines for a 
Pfaffian of the 3rd order : — 



I 



-> - 



12 ... 13 14 15 16 - 



23 - - - 24 



34 



25 • 



26 - 



35 36 



45 46 



56 



— > 1st frame-line 



2nd frame-line 



3rd frame-line 



- — > 4 th frame-line 



5 th frame-line 



6 th frame-line. 



It follows also that the rule for the formation of the terms is equivalent to a direc- 
tion that all possible products of n elements are to be taken, no two elements in any 
product being from the same frame-line. 

Thus, if in trying to form a term of the Pfaffian of the 3rd order whose elements 
are a, b, c, .... , m, n, o, we took, to commence with, the element a in the first row, we 
should thereby be debarred not only from taking anything else from this row (which is 
the first frame-line) but also from the second row (which is a part of the second frame- 
line), because a is an element in both, its place-name being 12. Our choice, conse- 
quently, would then be from among the elements left after deletion of these two lines, 
i.e., from 



54 



DR THOMAS MUIR ON 



/ 



- 9 - 



- % - - - 



m n 



and if we next decided on taking Jc, which is in the 3rd and 5th frame-lines, we could 
not thereafter take anything else from these lines — that is to say, we could not take j or 
I from the 3rd frame-line, or m or o from the 5th. We should thus be left with 



ahn 



as a term; and the number of inverted-pairs in the series 12 35 46 made up of the 
place-numbers of the chosen elements being 1 , the sign would be negative. 

(6) It is of interest to note, in passing, that the term composed of the 1st, 3rd, 5th, 

. . . elements in the hypotenuse of the semiquadrate array is always + , whatever the 

order of the Pfaffian may be, because the number of inverted-pairs in 12 34 56 . . . . 

is zero. Also, that the same is true of the term composed of the elements lying on the 

line which bisects the hypotenuse at right angles, because the series then to be 

considered is 

1,2k, 2,2fi-l, 3,2rc-2, n-\,n; 

and it is manifest that none of the pairs beginning with 1, 2, 3, . . . , n— 1 can be in- 
verted, and that, while those beginning with 2n, 2n—l,..., are all of them inverted, 
the number is in each case even. 

(7) With these preliminaries before us, let us now consider a fourth case of the 
theorem sought to be established, say the case where the Pfaffian is of the 5th order and 
the zero elements are in the places 12, 13, 23 — i.e., the Pfaffian 

I . . 14 15 16 17 18 19 It 

. 24 25 26 27 28 29 2t 

34 35 36 37 38 39 3t 

45 46 47 48 49 At 

56 57 58 59 5t 

67 68 69 U 

78 79 It 

89 8* 

9t 



A DEVELOPMENT OF A PFAFFIAN HAVING A VACANT MINOR. 



55 



Here the first three frame-lines, when freed of the portions containing zero elements, 
constitute a rectangular array of 3 rows and 7 columns, from which thirty-five (i.e., C 7)B ) 
determinants of the 3rd order are formable ; and the initial proposition to be made good 
is that every one of the 210 terms of these thirty-five determinants is a portion of a term 
.of the given Pfaffian. To do this we have only got to put in mental contiguity for a 
moment the definitions of a determinant and a Pfafnan : for each determinant term being 
required to consist of three elements taken from the rectangular array referred to, no 
two of which must belong to the same row or to the same column, complies with the 
requirement regarding the first three elements needed to form part of a term of the 
Pfaffian, viz., that they must be chosen from the first three frame-lines but that at the 
same time no two of them must belong to the same frame-line. The next proposition is 
that all the six terms of any particular one of the thirty-five determinants require the same 
cofactor in order that terms of the Pfaffian may be produced. This is made clear by con- 
sidering the fact that all of the six terms have their elements taken from the same set of 
frame-lines, and that the remaining two elements in each case must be chosen from the 
elements left when the said set has been deleted from the Pfaffian. Thus, if the 
particular determinant were 

15 17 18 

25 27 28 

35 37 38 



each of its terms could only become a term of the Pfaffian by having annexed to it two 
elements selected from those left when the 1st, 2nd, 3rd, 5th, 7th, 8th frame-lines of the 
Pfaffian have been deleted — that is to say, from 



46 49 it 

69 6* 

9t. 



We are thus prepared to advance a third proposition derived from the previous two, viz., 
that, apart from the question of sign, all the eighteen terms of each one of the products 
of the form 



15 


17 


18 


. 46 


49 


it 


25 


27 


28 




69 


6t 


35 


37 


38 






9t 



are terms of the Pfaffian. This means that 35 x 18, i.e., 630, terms of the Pfaffian are 
accounted for. Now the total number of terms in a Pfaffian of the 5th order is 1.3.5.7.9 ; 
the number of these which will vanish when the element 12 vanishes is 1.3.5.7 ; the 
additional number which will vanish when 13 vanishes is 1.3.5.7; and the additional 
number which will vanish when 23 vanishes is 1.3.5.7. It follows, therefore, that the 
total number of non- vanishing terms in the Pfaffian under discussion ought to be 



56 



DR THOMAS MUIR ON 





1.3.5.7.9 - 3(1.3.5.7), 


i.e., 


1.3.5.7(9 - 3), 


i.e., 


35 x 18; 



and this is exactly the number obtained from our development. 

(8) The only matters remaining now for consideration are those which concern the 
signs of the terms thus obtained, it being necessary for our purpose (1) to establish the 
fact that the eighteen signs of any product of the form 



15 


17 


18 


. | 46 49 U 


25 


27 


28 


69 U 


35 


37 


38 


9t 



are either all right or all wrong, and (2) to formulate a rule for distinguishing 
between products of these two kinds, so that the sign + may be prefixed to the one and 
— to the other. 

Now if no sign precede the product, the sign of any of the eighteen terms is 
determinable from the sign of the portion of the term which comes from the deter- 
minant factor and the sign of the portion which comes from the Pfaffian factor ; 
and the former being dependent upon the number of inverted-pairs in the series of 
column-numbers specifying the elements of the first part of the term, and the latter 
upon the number of inverted-pairs in the series of frame-line numbers specifying the 
elements of the second part of the term, it is clear that if <r be the sum of the said two 
numbers of inverted pairs the sign of the complete term will be ( — Y. On the other 
hand, the sign which it ought to bear as a term of the parent Pfaffian is fixed by the 
number v of inverted-pairs in the series of integers specifying the frame-lines of all 
the elements composing it. What is wanted, therefore, is a comparison of this number 
v with a- ; and, if we can show that v — a- is constant for all the eighteen terms, it will 
follow, of course, that the eighteen signs are either all right or all wrong. For 
example, in the product 



15 


17 


18 


.46 49 At 


25 


27 


28 


69 6* 


35 


37 


38 


9* 



— 17.25.38 is a term of the determinant and — 49.6t a term of the Pfaffian, the sign 

— in the one case being fixed by the number of inverted-pairs in 758 and in the 
other by the number in 496£, whereas the sign of the resulting term 17. 25. 38. 49. 6£ of 
the Pfaffian is fixed by the number of inverted-pairs in 172538496^. 

For ease in making the necessary comparison let us use 

I(a/3y....) 

to stand for the number of inversions found in the pairs of integers obtainable by 
placing each integer in front of those which follow it, and 

I(a/3y .... ; a'yS'y' . . . . ) 



A DEVELOPMENT OF A PFAFFIAN HAYING A VACANT MINOR. 57 

for the number of inversions found in the pairs obtainable by placing each integer 
of the first group in front of each integer of the second group. In the former, 
I(afiy . . .), the order in which we write the integers of the group is all-important ; in 
the latter, l(a/3y . . . ; a'fi'y. . . ), the order is of no consequence so long as we do not 
mix the two groups. 

With this notation a fundamental proposition regarding inverted-pairs, which bears 
directly on the subject in hand, can be stated very simply, viz., 

I(a/3y . . . a'/3'y' . - . ) = I(a/3y . . . ) + I(a'ySV • • • ) 

+ I(a0y...; a'/3V'...), 

and it is immediately evident therefrom that whatever interchanges may be made in 
the group a/3-y ... or in the group a/3'y. . . 

I(a(3y . . . a'/3'y' . . . ) - I(a/?y . . . ) - I(a'£y • • • ) 

will remain constant. 

As applied to the special groups of integers connected with the Pfaffian term 
above-mentioned this ensures that 

1(1725384960 - 1(172538) - 1(4960 

will not alter by reason of any interchanges taking place in the group 172538 or in 
the group 496L If in addition the integers 123 in the first group be excluded from 
interchange, we shall have 

1(172538) = 1(7; 23) + 1(5; 2) + 1(758), 
= 3 + 1(758), 

through all interchanges in 758. By substitution it therefore follows that the number 

1(1725384960 - 1(758) - 1(4960 

will remain constant while interchanges take place in 758 or in 496t ; and this is 
equivalent to saying that the terms of the parent Pfaffian which are obtainable from 
the product 

15 17 18 | . | 46 49 it 

25 27 28 69 6t 

35 37 38 I 9* 

are either all correctly or all incorrectly signed. 

If the said constant be even, the sign which ought to precede the product will of 
course be + , in the other possibility - . As a matter of practice, however, the easiest 
way of determining the sign to be placed in front of any product is to make the 
sign such that one of the terms obtainable from the product shall be correctly signed, 
and for this purpose the facts given in § 6 will be found useful. If the whole expan- 
sion be wanted, and the products be arranged in the natural order — that is to say, 
in such a way that the series of determinant factors shall begin with j 14 25 36 | 

VOL. XL. PART I. (NO. 5). I 



58 DR MUIR ON A DEVELOPMENT OF A PFAFFIAN HAVING A VACANT MINOR. 

and end with | 18 29 3t \ , the sign to be prefixed to any product is easily known 
from that of the preceding product. 

(9) The number of different forms of this new development which are possible 
in the case of a Pfafiian of the n th order is of course the number of partitions of 
the integer n into two integers, the first of the latter corresponding to the order of 
the determinant factors in the development, and the other to the order of the 
Pfaffian cofactors. For example, in the case of the Pfaffian of the 5th order we shall 
have the five developments 

(a) + 12J| 3456789* | - 13J| 2456789* | + (C 9>1 terms) , 

(/?) - | 13 24 |.'| 56789* | + | 13 25 |.'| 46789* | - (C 8;2 terms) , 

(y) - | 14 25 36 |.'| 789* | + | 14 25 37 |.'| 689* | - (C 7>8 terms) , 

(8) + | 15 26 37 48 |.9* - | 15 26 37 49 |.8* + (C 6>4 terms) , 

(e) +|162738495*| (C 5>5 term) , 

the parent Pfaffian containing no zero elements in the first case, 1 in the second, 
1+2 in the third, 1 + 2 + 3 in the fourth, and 1+2 + 3 + 4 in the fifth. 

The single elements in the first development may be viewed as determinants of 
the 1st order and in the fourth development as Pfaffians of that order. 



( 59 ) 



VI. — Contributions to the Craniology of the People of the Empire of India. 
Part II. The Aborigines of Chilta Ndgpiir and of the Central Provinces, the 
People of Orissa, the Veddahs and Negritos. By Professor Sir Wm, Turnek, 
K.C.B., D.C.L., F.R.S. (With Four Plates.) 

(Read July 2, 1900.) 

It is my intention in this, the second part of my memoir on the Craniology of the 
Races of India, to give the results of my examination of skulls obtained from the 
districts occupied by the aboriginal tribes in Chiita Nagpur, the Central Provinces, 
the people in the province of Orissa, and to compare them with the skulls of some 
other aboriginal people. 

The majority of the specimens described belong to the Indian Museum, Calcutta, 
and through the courtesy of the Trustees I was permitted to have them on loan 
for purposes of study. Many of these crania had been those of persons who had 
died in jail. The names, tribes, and castes, and not unfrequently the age, stature, and 
other physical characters, had been recorded in the prison books, and were embodied in 
the lists which were sent to me along with the skulls by the authorities of the museum. 
Several of these skulls were especially interesting, as having been presented to the 
museum by Colonel Dalton, the author of the valuable treatise on the Ethnology of 
Bengal. Other specimens in the museum had been obtained from the Medical College, 
Calcutta, and several were presented by Professor D. B. Smith ; in all probability they 
were from bodies which had been used for anatomical purposes. Mr W. H. P. Driver 
also had presented a series of crania from Ranchi. 

In addition, I have received specimens from former students holding appointments 
in the Indian Medical Service, and I take this opportunity of acknowledging their 
courtesy in presenting them to me. 

The descriptions in this part of my contribution to Indian Craniology are based on 
the examination of one hundred and one skulls, and the measurements are recorded 
in the series of Tables. 

The works which I have chiefly consulted in drawing up the account of the geo- 
graphical distribution and tribal characters of the aborigines, are Colonel Dalton's 
Descriptive Ethnology of Bengal, Calcutta, 1872; Sir W. W. Hunter's Statistical 
Account of Bengal and Imperial Gazetteer of India ; Sir H. M. Elliot's Memoirs 
of the Paces of the North- West Provinces of India, edited by John Beames, London, 
1869 ; Hie Tribes and Castes of Bengal, Ethnographic Glossary, and Anthropometric 
Data, Calcutta, 1891, by H. H. Risley, I.C.S. ; The Tribes and Castes of the North- 
western Provinces and Oudh, by W. Crooke, B.A., B.C.S., Calcutta, 1896 ; "India," 
by Sir Richard Temple in Chambers's Encyclopaedia; Census of India, 1891, General 
Report by Census Commissioner J. A. Baines, I.C.S. ; Report on the Lower Provinces 
VOL. XL. PART I. (NO. 6). K 



60 PROFESSOR SIR W. , TURNER ON 

of Bengal and their Feudatories, by C. J. O'Donnell, M.A., l.C.S. ; Report on the 
Central Provinces and Feudatories, by B. Robertson, l.C.S. ; Reports on Anthro- 
pology in Bulletin of Madras Government Museum, Madras, 1897-1900, by Edgar 
Thurston; The Distribution of the Negritos, by A. B. Meyer, M.D., Dresden, 1899. 

Aborigines. 

Before I enter on the description of the craniological characters of the different 
aboriginal tribes, it will be useful to say something of the geographical position of the 
districts in which they live, and of the distribution and physical characteristics of the 
people of each tribe. 

Chuta Nagpur is a division of Bengal situated to the south of Mirzapur, in the 
North- West Provinces, and to the north and east of the Central Provinces. It con- 
tains, amongst others, the districts of Singbhum, Manbhum, Hazaribagh and the 
tributary state of Sargiija, from all of which skulls had been obtained. In the 
Lohardaga district is the town of Ranchi, where there is an important jail, from which 
had been procured the crania of some prisoners who had been executed or had died 
of disease — many of whom were natives of the adjoining villages. The country is 
broken up into hills, valleys, and raised plateaux. Hindus form the largest element 
of the population, but interspersed among them are semi-Hinduised natives 
and aboriginal tribes. 

The Central Provinces are a large territory which extends as far south as the 
Godavery River, the Nizam's dominions, and the north part of the Madras Presidency. 
Skulls have been examined from Bastar, Raipur, and other districts in the provinces. 
The country is diversified and contains tablelands, which in some parts are 2000 feet 
high, ranges of hills, valleys, and wide plains. The Hindus are the preponderating 
element amongst the people, but numbers of aborigines are to be found, especially on 
the Satpura plateau and in the hill districts of the feudatory state of Bastar. 

Orissa is an extensive province on the west side of the Bay of Bengal, and is 
bounded on the west by Chuta Nagpur and the Central Provinces. Along the coast 
line it possesses a border of alluvial land, but the interior is an undulating country 
intersected by ranges of hills, the highest peaks of which are from 3000 to 4000 feet. 
Hindus constitute the mass of the people, but the aborigines and semi-Hinduised 
aboriginal tribes form an important element. Skulls have been obtained from 
Keunjhar, Kandh-mals, Cuttack, and other parts of Orissa. 

In the several provinces under consideration the Hindus occupy and cultivate the 
valleys and more fertile lands. The aboriginal tribes live in the hills and on the 
higher plateaux, and preserve more or less completely their religion and tribal customs. 
Where the Hindus have come into immediate contact with the aborigines, the latter, 
whilst retaining to some extent their ancient forms of faith and customs, have, in other 
respects, adopted the Hindu religion and modes of thought. 



CRANIOLOGY OF PEOPLE OF INDIA. 61 

Writers on the philology and ethnology of the people of India have distinguished, 
by the names Dravidian and Kolarian, two groups of languages spoken by the ab- 
original tribes who occupy the hill ranges in the Central Provinces, Chuta Nagpur, 
Orissa, extending also into Western Bengal and Southern India. The name Dravidian 
was given to the southern of the two linguistic groups by Bishop Caldwell, and many 
writers have attached to it an ethnological value. This group of languages is most 
extensively represented in the Madras Presidency, where it forms the south Dravidian 
group, known as Telugu, Tamil, Kanarese, and Malayalam ; but it also extends into the 
hill ranges in the Central Provinces and Orissa, as the north Dravidian group spoken by 
the Gonds, Tulus, Oraons, Kharwars, M&1 -Pah arias, and Kandhs. The Kolarian group 
of languages, as it has been named by Sir George Campbell,* prevails amongst the tribes 
which lie to the north of those who speak Dravidian, and who occupy the hill tracts of 
Western Bengal and Central India. The Santals, Mundas, Hos, Kols, Korwas, and 
Bhils are the principal tribes to employ the languages of this group. It by no means, 
however, follows that tribes speaking a Kolarian dialect are ethnically distinct from 
those who speak Dravidian, as it is not uncommon to find that a tribe possessing the 
physical characteristics of the Dravidians is classed linguistically as Kolarian. The 
division, therefore, into these two linguistic groups has a philological rather than an 
ethnological significance. Dravidian dialects are apparently spoken by about one-fifth 
of the population of India ; Kolarian by about one-tenth. 



Gond. Table I. 

These people are regarded on linguistic grounds as Dravidian. They inhabit 
an extensive tract of country formerly known as Gondwana, which extended from the 
Vindhyan mountains to the Godavery, and which now constitutes a large part of the 
Central Provinces. They are found also in the southern part of Chuta Nagpur and a 
small number in Orissa. They occupy the tableland of Satpura and the hill country 
from Mandla to Asirgarh, as well as Korea, Sirguja, and Udaipur. They were a brave 
and independent people before the rise of the Mogul Empire. Whilst some still retain 
their independence and original faith, others have been subjugated and have become 
either Hinduised or Mahomedans. Colonel Dalton considers the Marias who inhabit 
dense jungles in Bastar, Chanda, and other southern dependencies to be the best type 
of the primitive aboriginal Gond.t Along with the Rev. G. Hislop, he describes the 
wild Gonds as having flat noses, distended nostrils, thick lips, dark skin, scanty beard 
and moustache, and straight, black hair ; sometimes the hair is said to be short, crisp, 
and curly, but quite distinct from the woolly hair of the negro. In some instances the 
head is shaved, leaving only a top-knot, but more frequently the hair is matted and 

* Races of India. Journ. Ethno. Soc, London. N.S. Vol. I. p. 130, 1869. 

t See also Chanda Settlement Report ; Colonel Glasfurd's Report on Bastar ; Mr Robertson's Census Report, 1891. 



02 PROFESSOR SIR W. TURNER ON 

untidy. The Gonds are about the same height as the Marias and Bhatras, but are 
larger and heavier in build than the Onions or Kols. They are scantily clothed and the 
women are tattooed. The dead are cremated and the ashes are then buried, but it is 
said that the women and children are buried without being cremated. The grave is 
duff so that the head lies to the south and the feet to the north. In character, the 
Gonds are reserved, sullen, and suspicious, and the Marias are a shy, timid people. 
They are totemistic and exogamous. They practise both infant and adult marriage, 
and widows remarry. The unmarried young men sleep in a common dormitory, and 
in some villages there is a similar provision for the unmarried young women. Dalton 
says that they are indifferent cultivators, and careless about the appearance of their 
houses. The Gonds, who are not Hinduised, worship their own deities and the spirits 
of the forests in which they live. From the Census Report of 1891, it would appear 
that 1,379,580 people were returned as speaking the Gond branch of the northern 
Dravidian group of languages, though the actual numerical strength of the Gonds is 
said to be 2,897,591. 

The Edinburgh University Anatomical Museum contains four skulls of Gonds from 
the Godavery district, though the exact locality is not known. They had originally 
been in the collection of the late Dr Handyside, and were marked " wild tribes called 
Gotten or Gond, from Godavery district of Central India." They were all adults, 
though the wisdom teeth were not erupted in D ; three were presumably males and 
one a female. 

Norma Verticalis. — The crania had a marked family likeness. They were 
elongated, narrow, with vertical sides, and dolichocephalic in form and proportions. 
In the males the parietal eminences were feeble, in the female (C) they were more pro- 
jecting and gave greater relative breadth to the cranium. In both sexes they were 
situated considerably in front of the occipital point. The vault of the skull was some- 
what roof-shaped, but not ridged in the sagittal line. The skulls were cryptozygous or 
nearly so. In three specimens the Stephanie diameter was greater than the asterionic. 

Norma Lateralis. — The skulls rested behind on the cerebellar part of the occiput. 
The glabella and supra-orbital ridges, although visible, were not prominent even in the 
men. The forehead in the males only slightly receded ; in the female it bulged slightly 
forward. The antero-posterior curve of the cranial vault rose gently to the vertex, and 
from the obelion it sloped downwards and backwards into the occipital squama, which 
projected behind the in ion. There was no sign of parieto-occipital flattening. The 
frontal longitudinal arc in each skull was slightly less than the parietal, but always 
considerably in excess of the occipital arc. 

The nasal bones were of moderate size, with the bridge not prominent and concave 
forwards ; the fronto-nasal suture was not depressed, and the nasal spine of the superior 
maxillae was moderate. The junction of the side walls and floor of the anterior nares 
was rounded, and in three specimens the floor of the nose was separated from the 
incisive region of the maxilla by a low ridge. The canine and incisor fossae were of 



CRANIOLOGY OF PEOPLE OF INDIA. 63 

moderate depth. The teeth were fully erupted except in D, in which the wisdoms had 
not appeared, and they were in good order except in B, in which the crowns were much 
worn. No skull was metopic, but the other cranial sutures were distinct and denticu- 
lated. In two skulls Wormian bones were in the lambdoidal suture, and in one also in 
the parieto-mastoid suture. In all, the ali-sphenoid and parietal articulated at the 
pterion, but in C the junction was very narrow; in B a very small epipteric bone was 
present in the suture. The muscular ridges and. processes were not strong except in A. 
No skull had a 3rd occipital condyle or an exostosis in the external auditory meatus, 
or a subdivision of the malar bone. One skull had a pair of short para-mastoid pro- 
cesses : two had infra-orbital sutures. The interzygomatic breadth of the face invariably 
exceeded the intermalar, Stephanie, and asterionic breadth ; in A the interzygomatic 
breadth was slightly in excess of the parieto-squamous, and in B they were almost 
equal. 

The lower jaw was moderate in size and with a deep symphysis in B ; the chin was 
prominent ; the coronoid height did not greatly exceed the condyloid. The intergonial 
width and gonio-symphysial length closely approximated to each other. 

The mean cephalic index was 71 '2 and the range of variation was from 69*4 to 75. 
The crania were therefore dolichocephalic. The greatest length of the crania ranged from 
176 to 180 mm., and the mean was 177*5 ; the greatest breadth ranged from 123 to 
132 mm., and the mean was 126*5. The vertical index was 76, and the range of varia- 
tion was from 7 4 "6 to 77'2. The crania were metriocephalic. The actual height of 
the skulls ranged from 132 to 139 mm., and the mean was 135. In each skull the 
basi-bregmatic height was greater than the parieto-squamous breadth. 

The nasio-mental length ranged from 98 to 112 mm., with a mean of 104 mm. ; the 
interzygomatic breadth ranged from 118 to 128 mm., with a mean of 121*5. The com- 
plete facial index ranged from 797 to 91 -8, with a mean of 84*8 ; the skulls, therefore, 
were chamseprosopic or low-faced. The maxillary or upper facial index ranged from 
46*9 to 53*4, with a mean of 50'2 ; in the proportion of its upper region, the face was 
in the lowest term of the leptoprosopic group. 

• The mean gnathic index was 99*8, and the range of variation was from 96*9 to 
104*4 ; the skulls, therefore, on the average, were mesognathous, though one was 
orthognathous and another prognathous. The mean nasal index was 53*4, and the 
range of variation was from 48*9 to 56*8 ; though the mean was just within the platy- 
rhine group, two of the crania were mesorhine. The mean orbital index was 83, and 
the range of variation was from 81*1 to 83*8. All the orbits were microseme. The 
mean palato -maxillary index was 114*5, and the range of variation was from 105*3 to 
122; the greatest palato-maxillary length was 56 mm. and the greatest breadth was 
61 mm.; the skulls were in the mean mesuranic, though one was dolichuranic and tw r o 
brachyuranic. 

The mean cubic capacity of the four crania was 1274*5 cub. cent, i.e., microcephalic, 
to which category each cranium belonged. 



64 



PEOFESSOR SIR W. TURNER ON 



Table I. 

Dravidian Tribes. 















Onion. 


Paharia, 
Birbhum. 


Kharwar 
Bogta. 


Kandh. 




bo 


V 

bo 


«5 
SO 
















Gond. 






so 




.* 


eS 


Fh 




75 












O °3 

o 

M 


ft 

la 


o 

S 
ce 

O 


o 

5 


% 

o 
A 
P 


C3 

w 




2 cf 

^1 






KU.A.M. 




I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I M. 


I.M. 


E.U.A.M. 


Collection number, 


A. 


B. 


C. 


D. 


608 


610 


601 


559 


558 


551 


556 




Age, 


Ad. 


Ad. 


Ad. 


Ad. 


Ad. 


Ad. 


Ad. 


50 


Aged. 


29 


Ad. 


25 


Sex, ..... 


M. 


M. 


F. 


M. 


M. 


M. 


F. (?) 


M. 


M. 


M. 


F. 


M. 


Cubic capacity, 


1238 


1250 


1295 


1315 


1420 


1430 


1250 


1246 


1206 


1305 


1070 


1325 


Glabello-occipital length, 


180 


177 


176 


177 


186 


189 


175 


176 


178 


175 


158 


172 


Basi-bregmatic height, . 


139 


132 


134 


135 


130 


136 


127 


124 


128 


128 


123 


140 


Vertical Index, 


77-2 


74-6 


76-1 


76-3 


69-9 


72- 


72-6 


70-5 


71-9 


73-1 


77-4 


81-4 


Minimum frontal diameter, . 


92 


92 


91 


89 


91 


90 


92 


88 


91 


85 


92 


92 


Stephanie, .... 


110 


110 


105 


101 


104 


104 


105 


102 


102 


101 


115 


106 


Asterionic, .... 


102 


101 


100 


103 


103 


106 


104 


108 


108 


104 


90 


106 


Greatest parieto-squamous 


























breadth, .... 


125p. 


123s. 


132p. 


126p. 


132s. 


129s. 


132p. 


135s. 


128s. 


128s. 


133p. 


135s. 


Cephalic Index, . 


69- 4 


69-5 


75-0 


71-2 


71' 


08-3 


75-4 


76-7 


71-9 


73-1 


84-2 


78-5 


Horizontal circumference, 


500 


493 


488 


488 


503 


518 


480 


497 


498 


490 


463 


483 


Frontal longitudinal arc, 


135 


132 


130 


130 


130 


128 


118 


127 


118 


123 


110 


119 


Parietal „ ,, 
Occipital „ „ 


140 
103 


J243 


132 
108 


131 
114 


126 
121 


147 
110 


J234 


118 
109 


130 
112 


124 
115 


127 
105 


120 
119 


Total 


378 


375 


370 


375 


377 


385 


352 


354 


360 


362 


342 


358 


Vertical transverse arc, 


298 


298 


298 


299 


305 


304 


290 


292 


280 


294 


287 


296 


Length of foramen magnum, 


29 


34 


32 


33 


30 


35 


33 


35 


33 


37 


28 


37 


Basi-nasal length, 


104 


91 


95 


97 


103 


101 


95 


96 


98 


91 


88 


99 


Basi-alveolar length, 


102 


95 


95 


94 


98 




91 


95 




84 


89 


95 


Gnathic Index, 


98-1 


104-4 


loo- 


96-9 


95-1 




95-8 


99- 




92-3 


101-1 


96- 


Interzygomatic breadth, 


128 


122 


ns 


118 


127 


130 


123 


129 


134 


121 


115 


128 


Intermalar ,, 


117 


113 


109 


109 


115 


124 


108 


111 


124 


112 


106 


116 


Nasio-mental length, 


102 


112 




98 


108 


126 








107 




108 


Nasio-alveolar ,, 


60 


64 


63 


57 


64 




61 


64 




62 


51 


64 


Complete Facial Index, 


79-7 


91-8 




83' 


85' 


96 


• . . 






88- 




84-3 


Nasal height, 


47 


46 


44 


43 


48 


50 


46 


48 


45 


47 


37 


47 


Nasal width, 


23 


24 


25 


24 


26 


27 


22 


25 


26 


23 


25 


25 


Nasal Index, 


48-9 


52-2 


56-8 


55-8 


64-2 


54- 


47-8 


52-1 


57-8 


48-9 


67-6 


53-2 


Orbital width, 


36 


37 


37 


37 


37 


37 


36 


39 


41 


38 


35 


40 


Orbital height, 


30 


30 


31 


31 


31 


33 


30 


32 


31 


35 


27 


32 


Orbital Index, 


83-3 


81-1 


83-8 


83-8 


83-8 


89-2 


83-3 


82' 


75-6 


92-1 


77-1 


80- 


Palato-maxillary length, 


55 


56 


50 


50 


52 




48 


51 




49 


50 


52 


Palatomaxillary breadth, 


61 


59 


61 


60 


67 


72 


55 






65 


60 


68 


Palato-maxillary Index, 


110-9 


105-3 


122- 


120- 


128-8 


• . . 


114-5 






132-6 


120- 


130-7 




' Symphysial height, 


29 


35 




28 


27 










27 




33 




Coronoid ,, 


69 


63 




55 


57 


72 


. . . 


54 




53 




62 


c3 


Condyloid ,, 


60 


61 


.. . 


53 


60 


67 




59 




50 




61 




Gonio-symphysial length, 


88 


87 




84 


80 


90 




77 




78 




81 


5 " 


Inter-gonial width, out- 


























o 


side, 


89 


87 




79 


89 


106 


* . . 


86 




89 




100 


>— 1 


Breadth of ascending 




























ramus, 


32 


32 


... 


31 


33 


34 




30 




27 




35 



Note. — In the Tables, as in Part I., I.M. signifies Indian Museum ; E.U.A.M., Edinburgh University Anatomical 
Museum; H.T., Henderson Trust-Collection; T.C.D., Trinity College, Dublin. 



CRANIOLOGY OF PEOPLE OF INDIA. 65 



Ordon. Table I. 

The Oraons, or Uraons, are a Dravidian tribe in Chiita Nagpiir, especially in the 
tributary states of Sirguja and Jashpur, but scattered also in Singbhum, Manbhum, and 
Hazaribagh. The tradition in the tribe is that they migrated from the west coast of 
India. Dalton states that the skin is a dark brown approaching black ; the hair is 
long, black, coarse, and inclined to be frizzy ; the jaws are projecting ; the lips are 
thick ; the forehead is low, narrow, and not receding ; the eyes are bright but not 
oblique ; the expression is pleasing ; and the upper face displays intelligence. Dalton 
gives the height of a young man as 5 feet 2 inches, and that of four girls between 12 
and 16 years as ranging from 4 feet 7 J inches to 5 feet |- inch. The dress of the men 
is a long strip of cloth adjusted about the middle of the body, but giving free play to 
the limbs, and a girdle of cord is about the waist. The hair is gathered into a knot at 
the back of the head, in the knot are combs and ornaments of brass and glass ; bright 
brass chains dangle from the ears. The women wear a waist-cloth, and when more 
civilised, a cotton dress, and ornament themselves with beads and copper or brass rings. 
They have tattoo marks on the brow and temple, and on the arms and back. The 
unmarried men sleep in a bachelor house, the Dhumkiiria, and it is probable that the 
young women have a similar arrangement. Adult marriage is practised, and widows 
may remarry. The dead are cremated, and the ashes are collected in an earthern vessel, 
which for a time is suspended to a post in front of the house of the deceased, but is 
subsequently buried. They eat flesh as well as vegetables. They worship a supreme 
being as represented by the sun. In the General Report on the Census of India, 1891, 
it is stated that 368,222 speak the tribal language, but that the numerical strength of 
the Oraons is 523,258. 

Three skulls in the Indian Museum, obtained from the neighbourhood of Eanchi, 
are marked Onion or Uraon : No. 601, from the village of Chandoa, 30 miles from Ran- 
chi ; No. 606 from Konka village; and No. 610 marked Jura from Lalpur village. 
They were presented by Mr W. H. P. Driver. They are all adult ; I regarded two as 
males, but the sex of the skull from Chandoa was more doubtful. 

In their general form they were elongated and ovoid, and with vertical sides, and 
resembled in general form the skulls of the Miinda race, also from Ranchi, to be 
described in a subsequent section. One was hyper-dolichocephalic, and the parietal 
longitudinal arc greatly exceeded the frontal and occipital ; another was dolichocephalic 
with the frontal arc a little the longest ; the third slightly exceeded the upper numerical 
limit of the dolichocephalic, and in it the parietal and occipital arcs could not be pro- 
perly differentiated. In two specimens the basi-bregmatic diameter was less than the 
parieto-squamous, but in the hyper-dolichocephalic skull it was greater. The face was 
orthognathous. In two specimens the nose was platyrhine ; in the third it was lepto- 
rhine. In two skulls the orbital proportions were microseme, in the third just within 



6G PROFESSOR SIR W. TURNER ON 

the megaseme group. The palato-maxillary index in one was mesuranic, in another 
brachyuranic. The face in one was chamseprosopic, in the other leptoprosopic. In the 
two males the mean capacity of the cranium was relatively high for an aboriginal race, 
viz., 1425 c.c. ; in the possible female skull the capacity was 1250 c.c. 

Male Pahdrid or Hillmen of Rdjmahdl. Table I. 

Dalton, in the Ethnology of Bengal, devotes a section in his chapter on the 
Dravidian tribes to the aborigines who inhabit the Rajmahal Hills. This range 
extends from the banks of the Ganges to the Brrilrmani river and the boundary of the 
Birbhum district, and is in the Santal Parganas district of Bengal. He also states that 
in the Ramgarh Hills of the Birbhum district, and at the foot of the Rajmahal Hills, are 
villages occupied by a tribe who call themselves Mal-Paharias, — the precise affinities of 
which it is somewhat difficult to determine. As two skulls of aborigines marked Paharias 
from Birbhum have come under my observation, it is convenient, from their possible 
Dravidian affinities, to consider them in this section. The Malers are short in stature, 
face oval, nose not prominent but broad below, and with the nares circular rather than 
elliptical ; lips full, eyes not oblique. They dress as well as the peasants of the plains, 
and the women wear a white skirt, a gay coloured square of silk over the right shoulder 
and tied under the left arm. The hair is collected into a knot behind the head, with 
two long locks hanging over the ears. They are apparently exogamous. Marriage is 
either infant or adult, and widows can remarry. A special house is provided for the 
bachelors, and another for the unmarried girls. They worship the sun and their 
ancestors, and believe in the transmigration of souls. The dead are sometimes buried, 
though, Mr Risley says, more usually cremated. They are hunters, but they also prac- 
tise jhtim cultivation. They eat flesh as well as vegetables, and drink a fermented 
liquor. The numerical strength of the tribe is said to be 18,506, though 30,838 use 
the tribal language. 

In the collection in the Indian Museum are the skulls of two men, Nos. 558, 559, 
from Birbhum, both of whom had died in the prison hospital. No. 558, marked 
Dhobia Paharia, was that of a man said to be 80 years old, with an edentulous upper 
jaw ; he had sustained a comminuted fracture of the frontal bone, the pieces of which 
had subsequently united. No. 559, also marked Paharia, was named Rampoojar, and 
aged 50. 

The skulls were not roof-shaped, but were somewhat flattened at the vertex, and 
the outline was ovoid in the norma verticalis, though the cranium in one was not 
specially elongated, and the side walls bulged somewhat in the squamous region. In 
No. 558 the length-breadth index was 71 '9, dolichocephalic, and the parietal longitu- 
dinal are greatly exceeded both the frontal and occipital ; the vertical index corresponded 
with the cephalic. In No. 559 the length-breadth index was 767 in the lower term of 
the mesaticephalic group ; in this skull the frontal longitudinal arc greatly exceeded 



CRANIOLOGY OF PEOPLE OF INDIA. 67 

the parietal and occipital ; the vertical index was much below the cephalic. The glabella 
and supra-orbital ridges were more prominent in the aged than in the younger man. 
In both the forehead slightly receded. In the old skull the parieto-occipital region was 
asymmetrical as if from artificial pressure, but in the other it had a gentle slope 
backwards. The nasion was not depressed, and the bridge of the nose, concave from 
above downwards, was distinct, though less so in the old man. The nose was 
platyrhine in the old skull, 57*8, and nearly so in the adult — viz., 52*1, in which also 
the upper jaw was mesognathous. In both the orbital index was mesoseme. The 
muscular ridges were stronger in the aged skull, which was markedly phsenozygous, and 
wide both in the interzygomatic and intermalar diameters ; it rested behind on the 
mastoids. The adult cranium was nearly cryptozygous, and rested behind on the 
occipital bone. In both the cubic capacity was small, the mean of the two being 
1226 c.c. 

Kharwdr. Table I. 

In Chiita Nagpur and Southern Behar is a non- Aryan tribe named Kharwar, who 
speak a Kolarian tongue. The Bhogtas are the most important division of the tribe. 
Dalton states that the Kharwars are mixed up with the Cheros, living in the same 
district, with whom they claim affinity. Both have become proselytes to Hinduism. 
When visited in 1794 by Captain J. T. Blunt, they were seen to be nearly naked, and 
armed with bows, arrows, and hatchets. Buchanan found that whilst some were land- 
owners and others labourers, there were others again who were obviously primitive in- 
habits, and represented the aboriginal inhabitants. The low Kharwars are said by 
Dalton to resemble strongly the Santals. The skin was very dark, nose low and 
pyramidal-shaped, lips thick and protuberant, zygomata so prominent that the temples 
were hollow. Another observer says that the hair was black and straight. The 
facial type is much more refined in the land-owning class, owing to intermarriage with 
high castes. The women are tattooed as in other Dravidian tribes. The Kharwars are 
totemistic, and marriage within the same sect is forbidden. They have in a large 
measure adopted the Hindu practice of infant marriage ; in the more primitive tribes 
the marriage of widows is permitted. Some of the clans continue to offer sacrifices to 
spirits. They practise cremation, and throw the ashes into a running stream. They 
will not eat flesh, but cultivate the soil for grain. According to the Census Report 
for 1891, their numerical strength was 112,298, but only 7651 spoke the tribal 
language. 

The Indian Museum contains a skull, No. 551, of a man named Bahadur of the 
Bhogta division of the Kharwar tribe. He came from Gola, Hazaribagh, Chuta Nagpur. 
He was reported as 29 years old, 5 feet 0'5 inch high ; eyes brown, not very almond 
shaped ; beard very scanty, slight moustache, no whiskers ; lips everted ; nose pyra- 
midal ; cheek bones prominent. He died of phthisis, and is said to have been a poor 
example of his race. The skull was presented by Dr J. Wood. 

VOL. XL. PART I. (NO. 6). L 



68 PROFESSOR SIR W. TURNER ON 

The cranium was an elongated ovoid, though the sides were not so vertical as in 
many dolichocephalic skulls of the aborigines ; the parieto-squamous diameter was con- 
siderably greater than the Stephanie ; a low sagittal ridge was associated with a 
moderate slope outwards to the parietal eminences. The length-breadth index, 73*1, 
was dolichocephalic, and the frontal and parietal longitudinal arcs were almost of the 
same length ; the breadth and height were equal. The forehead was retreating ; the 
glabella and supra-orbital ridges were moderate. The slope downwards from the 
obelion was steeper than in the more dolichocephalic crania ; the occipital squama was 
prominent and projected behind the inion. The nasion was not depressed ; the bridge 
of the nose was sharp and laterally compressed ; the nasal spine of the superior maxillae 
was strong, and a sharp ridge separated the floor of the nose from the incisive region 
of the jaw. The nasal index, 48*9, was almost leptorhine, and the gnathic index, 92*3, 
was orthognathic. The orbital index, 92*1, showed the height of the orbit to be 
almost equal to its breadth; the palato-alveolar arch, 132*6, was strongly brachy- 
uranic. In its complete facial index, 88, the face was chamseprosopic. The upper 
wisdom teeth were fully erupted, the lower were appearing ; the upper incisive fossae 
were deep. The skull was not metopic ; there were no Wormian bones. A small 
epipteric bone was in the left pterion. The hard palate was strongly arched ; the 
occipital condyles were flattened ; the left jugular foramen was partially blocked by a 
growth from the petrous-temporal ; the left jugal process was tuberculated. The lower 
jaw was feeble. The skull was cryptozygous, and rested behind on its lower occipital 
surface. The cubic capacity was 1305 c.c, and the cranium was microcephalic. 

Kandh. Table I. 

The Kandhs, Kondhs, or Khonds are regarded as Dravidians. The name signifies 
mountaineer, and they constitute one of the most important aboriginal tribes in Orissa, 
where they occupy an elevated plateau, intersected by ranges of hills called Kandhmals ; 
but they are also scattered through the tributary states of Orissa. An interesting 
account of the people and their customs has been given both by Major Macpherson and 
by Colonel Dalton. The latter writer states that the men are physically a fine race, more 
so than the Gonds, Bhuiy&s, and Pans. They are as tall as the average Hindu, and 
not much darker in complexion. He regards them as a mixed race, a blend of the 
Kol, Gond, and Aryan. They worship their own deities, one of the most important 
being the earth-god or goddess. They are an agricultural people, and before they 
came under British influence they made human sacrifices to the earth-goddess, and 
practised female infanticide. Their clothing is scanty, and consists of a waistcloth 
passed between the thighs. The long hair is tied into a horn-like projection between 
the eyes. The cheeks and forehead are tattooed. The Kandhs practise cremation. 
The unmarried young men have a common dormitory, and the girls also have a house 
assigned to them. Marriage is between adults, and not during infancy ; widows may 



CRANIOLOGY OF PEOPLE OF INDIA. 69 

remarry. They are inveterate drunkards. In the Census Report for 1891, 627,388 
persons are returned as Kandhs, though only 320,071 speak the tribal language. 

I ha,ve had the opportunity of examining two skulls said to be those of Kandhs. 
One was presented to me by a former pupil, now Major Wm. B. Bannerman, M.D. 
It was that of a man named Judisther Jani, an inhabitant of the village of Bhatpara, 
in the Khonda subdivision of the commissionership of Orissa. The man had been 
hanged for murder in the jail at Cuttack. Another specimen, No. 556, in the Indian 
Museum, was presented by Dr W. D. Stewart, and was obtained from the Kandhmals. 
It was that of a woman said to be 18 years old, and 5 feet 1 inch in stature. 

The male skull was that of an adult. The teeth were more worn in the upper 
jaw than in the lower. The sutures were unossified, and if it had not been for the 
worn condition of the molars, one would have regarded the man as about 30 years 
of age. 

In the norma verticalis the skull was broadly ovoid with no sagittal ridge, and 
with a moderate slope from the suture to the parietal eminences. In the proportion 
of length and breadth the cranium was mesaticephalic, 7 8 '5, and nearer therefore to 
the brachycephalic than the dolichocephalic standard. The parietal arc was only 
1 mm. longer than either the frontal or occipital. The height was greater than the 
breadth, and the vertical index was 81 '4, akrocephalic. 

In the norma lateralis the glabella and supra-orbital ridges were moderate, the 
forehead was slightly receding, the vertex was moderately arched, and the slope back- 
wards into the occipital squama was gentle. A slight want of symmetry was noticed 
in the occipital squama, but not sufficient to lead one to infer that there had been 
intentional parieto-occipital flattening. The skull was cryptozygous, and rested behind 
on the occipital condyles. The nasion was not depressed ; the nasal bones were slender, 
and the osseous bridge was depressed and slightly concave. The nasal spine of the 
superior maxillae was moderate, and the floor of the nose passed into the incisive region 
of the upper jaw without the interposition of a dividing ridge. The upper jaw was 
orthognathic. The complete facial index was 84*3, — i.e., chamseprosopic ; the nasal 
index was platyrhine, and the orbital index was microseme. The palate was remarkably 
deep and brachyuranic. The lower jaw was well formed and with a strong chin. A 
large epipteric bone was in each pterion. The cubic capacity of the cranium was micro- 
cephalic, 1325 c.c. 

The female skull, No. 556, from the Kandhmals, was that of a young woman, and 
the wisdom teeth were not erupted. A slight transverse constriction was seen behind 
the coronal suture. Its breadth was great in relation to the length. The parieto- 
occipital region was steepish but not flattened; the cephalic index, 84*2, placed it 
amongst the brachycephalic. The parietal arc was much longer than either the frontal 
or occipital. The vertex was flattened ; the frontal and parietal eminences were promi- 
nent, the forehead was vertical, all of which are sexual characters. The height was 
considerably below the breadth, and the vertical index was 77 '4. The bridge of the 



70 PROFESSOR SIR W. TURNER ON 

nose was wide and flattened ; the anterior nares were wide and rounded at the junction of 
the side walls with the floor ; the nasal index was strongly platyrhine. The upper jaw 
was mesognathous, the orbital index was microseme, and the palate was brachyuranic. 
The cranial capacity was only 1070 c.c. The skull was cryptozygous. 

Ndgesar or Kisdn. Table II. 

The Nagesars are a Dravidian tribe found in Sirguja, Jashpur, Palamau, and 
Lohardaga in Chuta Nagpur. Dalton says that in appearance they resemble the 
Kols, but not the best type, the Santal rather than the Ho. They are not, however, 
marked with a godna or arrow, and the women are not tattooed. Dalton describes 
them as ill-favoured, the forehead receding, narrow and low ; the nose short, broad at 
the base and with a truncated appearance ; the front teeth and jaws project, tilt up the 
lip and the end of the nose, and give a prognathic character. The skin is deep brown to 
black ; the stature is short. They are totemistic and practise adult marriage. They 
offer sacrifices to the sun and other deities, but many of them worship the tiger — like 
the Santals — and they also adore their ancestors. 

The Indian Museum contains the skull (No. 405) of a man set. 30, of the Nagesar 
tribe from Chuta Nagpur. He was a Dacoit named Lukroo, who died in prison. The 
skull was presented by Lieut. -Col. Dalton. 

The cranium in the norma verticalis was an elongated ovoid with vertical sides, a 
ridge-like sagittal region with a steep slope downwards and outwards to the parietal 
eminences. The cephalic index was only 67 "8, and the skull was hyper-dolichocephalic. 
The basi-bregmatic height materially exceeded the breadth, and the vertical index was 
7 3 "3. The glabella and supra-orbital ridges were moderate; the forehead somewhat re- 
ceded ; the parieto-occipital region sloped gradually backwards ; the occipital squama was 
rounded and projected behind the inion. The nasion was shallow ; the bridge of the 
nose was almost vertical and inclined to be flattened ; the nasal spine of the superior 
maxillae was feeble, and the anterior nares rounded off into the incisive region of the 
upper jaw. The nasal index, 53*2, was platyrhine, but the gnathic index, 96*9, was 
orthognathous. The complete facial index was 80*6, i.e., low-faced or chamaeprosopic. 
The height of the orbit was materially below the breadth, and the index, 84 '2, placed the 
orbit almost in the microseme group. The palato-maxillary index, 111*1, was almost 
dolichuranic. The teeth were fully erupted and showed signs of wear; the canine 
fossae were deep. The skull was not metopic, and the other sutures were not ossified ; 
a small inter-parietal bone and smaller Wormian bones were in the lambdoid region. In 
the left pterion were two epipteric bones, and the right alisphenoid was pointed. The 
os planum of the ethmoid was pointed in front. A pterygo-sphenoid foramen was 
present on the right side. The muscular ridges were moderate. A third condyle was 
not present, and the right jugal process was tuberculated. The cubic capacity of the 
cranium was only 1252 c.c, therefore distinctly microcephalic. 



CRANIOLOGY OF PEOPLE OF INDIA. 



U 



Table II. 



Dravidian Tribes. 





Nagesar. 






Bhuiya. 






Korwa. 


Tamil from 






Lukroo. 










Fukeera. 


Madras. 






I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


E.U.A.M. 


Collection number, 


405 




441 


439 


438 




404 


... 






Age, 


30 




Adult. 


Adult. 


Adult. 




28 


Ad. 


Ad. 




Sex, ..... 


M. 




M. 


M. 


F. 




M. 


M. 


M. 




Cubic capacity, . 


1252 




1438 


1330 


1255 






1150 


1240 




Glabello-occipital length, 


180 




189 


175 


177 




186 


181 


181 




Basi-bregmatic height, . 


132 




136 


142 


131 




137 


131 


132 




Vertical Index, . . 


73-8 




72-0 


81-1 


74-0 




73-7 


72-4 


72-9 




Minimum frontal diameter, . 


89 




95 


94 


89 




91 


90 


87 




Stephanie „ ,, 


108 




116 


112 


110 




105 


99 


102 




Asterionic „ „ 


102 




106 


109 


96 




107 


101 


95 




Greatest parieto-squamous 






















breadth, . . . . 


122s. 




132s. 


130s. 


133p. 




128p. 


121s. 


130s. 




Cephalic Index, . 


67-8 




69-8 


74-3 


75-1 




68-8 


66-9 


71-8 




Horizontal circumference, 


495 




520 


492 


490 




511 


490 


495 




Frontal longitudinal arc, 


120 




130 


128 


130 




130 


129 


123 




Occipital „ „ 
Parietal „ ,, 


J243 




J253 


[234 


125 
109 




138 
104 


125 
105 


130 
108 




Total ,, ,, 


363 




383 


362 


364 




372 


359 


361 




Vertical transverse arc, 


288 




302 


313 


305 




300 


273 


287 




Length of foramen magnum, 


33 




36 


34 


31 




36 


34 


35 




Basi-nasal length, 


98 




105 


103 


95 




105 


104 


105 




Basi-alveolar length, 




95 




100 


103 






99 


95 


101 




Gnathic Index, 




96-9 




95-2 


100- 






94S 


91-8 


96-2 




Interzygomatic breadth 




124 




131 


133 


115 




126 


123 


123 




Inter malar „ 




113 




117 


122 


103 




117 


115 


114 




Nasio-mental length, 




100 












106 


105 






Nasio-alveolar ,, 




62 




67 


65 








62 


59 


61 




Complete facial Index, 




80-6 














84- 


85-3 






Nasal height, 




47 




50 


50 








46 


47 


47 




Nasal width, 




25 




26 


25 








27 


27 


25 




Nasal Index, 




53-2 




52- 


50- 








58-7 


57-4 


53-2 




Orbital width, 




38 




38 


38 


40 




39 


39 


36 




Orbital height, 




32 




29 


31 


38 




28 


29 


30 




Orbital Index, 




84'2 




76-3 


81-6 


95- 




' 71-8 


74-4 


83-3 




Palato-maxillary length 




54 




56 


54 






54 


53 


53 




Palato-maxillary breadth, 


60 




65 


66 








65 


60 


62 




Palato-maxillary Index, 


111-1 




116' 


122-2 








120- 


118-2 


116- 






" Symphysial height, 


30 




• •• 


• • • 








29 


28 


• «• 




g- 


Coronoid ,, 


60 




• • • 


• • ■ 








57 


62 






•■""8 


Condyloid „ 


59 














54 


61 






£ ■{ Gonio-symphysial length, 


80 






• •■ 


, , 






90 


83 


• ■ ■ 






Inter-gonial width, outside 


, 93 








. . 






96 


91 






J 


Breadth of ascending 
ramus, 


29 




... 


... 


... 




29 


34 


... 





72 PROFESSOR SIR W. TURNER ON 



Bhuiyd. Table II. 

In addition to the name Bhuiya, these people are known by other appellations. 
Colonel Dalton uses as an alternative Bhiiniya, Mr Buchanan Hamilton calls them 
Bhungiya, Mr Bisley adopts the form Bhuiya, but gives a number of synonyms ; Mr 
"W. Crooke also names them Bhuiya. Mr Bisley considers the name to mean 
" children of the soil," and that it is not employed as a definite tribal designation, 
but as implying a status or connection with the land. Bhuiya is said to be a Sanskrit 
word, used over India from Assam to Rajputand, and from Madras to Behar, associated 
with some claim to land, a fact which Mr Risley regards as strongly supporting his 
contention. Mr O'Donnell, in his Census Report, p. 42, states that Bhuiya, from Bhui, 
land, is in Hindu terminology synonymous with autocthon. Colonel Dalton considers 
that in some parts of Chuta Nagpur the name has a tribal significance, and he links 
them with the Dravidians. He says that the lowest type have swarthy, almost black 
skins, and coarse negro-like features. In the Keunjhar hills they are apparently the 
dominant aboriginal people, and are described by Dalton as having the skin varying 
from deep chocolate to tawny ; very large mouths ; thick, projecting lips ; low, narrow 
foreheads ; eyes dark, well-shaped ; hair abundant on head but not on face ; stature 
short, averaging 5 feet 2 inches. The higher types found in Gangpur and Bonai are 
dark brown in colour ; hair black, straight, abundant on head, scanty on face ; stature 
moderate ; cheek and jaw bones projecting ; face broad and square ; nose rather 
retrousse, not very broad at the root ; mouth and teeth well formed ; eyes straight, 
not large or deeply set. 

In the tributary States the girls seldom marry before puberty, but in other parts 
the marriage age is twelve, and in the land-holding class during infancy. In some 
places the unmarried men have a common domicile, and the girls also have a house set 
apart for them. Widows may marry again. The wealthier classes are properly clothed, 
but amongst the more primitive people the raiment is very scanty. The women are 
tattooed. The dead are cremated and the ashes are thrown into an adjoining stream. 
They eat pork and fowls, but not the flesh of the cow or buffalo. Many of the 
Bhuiyas are Hinduised, others worship their ancestors. Mr Crooke states that the 
rules of succession do not differ from those of cognate Dravidian tribes. 

The Indian Museum contains three adult crania marked Bhuiya from Keunjhar in 
the Orissa Hills, presented by Dr W. D. Stewart in 1868. Two of these, Nos. 439, 
441, were males ; one, No. 438, was that of a woman. 

When examined in the norma verticalis the general form was an elongated ovoid, 
but the greater projection of the parietal eminences in the woman's skull raised its 
breadth to 133 mm., which in relation to the length gave it a cephalic index 75*1. In 
the two male skulls the index was 69 "8 and 74*3 respectively ; both were dolichocephalic. 
In the woman's skull and in one of the men the vertex was comparatively flat ; in the 



CRANIOLOGY OF PEOPLE OF INDIA. 73 

other man it was more roof-shaped, and the antero-posterior curve was higher at the 
vertex. The backward slope to the occipital point was more prolonged in the other 
crania. In the men the basi-bregmatic height exceeded the greatest breadth. In the 
woman it was somewhat less, and the greater parietal projection gave a pentagonal 
outline to the cranium, in which the frontal longitudinal arc was the longest. In the 
two men the large Wormian bones in the lambdoidal suture interfered with the measure- 
ments of the parietal and occipital longitudinal arcs. In two skulls a faint transverse 
depression behind the coronal suture indicated that a band had been worn during 
infancy. The forehead in the woman and in one man was almost vertical, but receded 
somewhat in the other male. The skulls were cryptozygous or nearly so, and rested 
behind on the occiput. The glabella and supra-orbital ridges only slightly projected. 
The nasion was not much depressed ; the nose had a definite bridge, concave for- 
wards ; the nasal spine of the superior maxillae was moderate. The nasal index in the 
two men was mesorhine, 52 and 50 respectively ; in the woman's skull the face was 
broken. In the men the orbital index was microseme, in the woman megaseme ; the 
palato-maxillary index was brachyuranic ; the gnathic index in one male was ortho- 
gnathous, in the other mesognathous. The teeth were erupted, though in one male the 
wisdoms were not fully in place. The cranial sutures were unossified ; epipteric bones 
were seen in two crania. In one male, stunted paramastoid processes were present. In 
the female skull each occipital condyle was almost equally divided by a constriction 
into an anterior and a posterior area. The cubic capacity of the female skull was 
1255 c.c, and the mean of the two males was 1384 c.c. 

Korwd. Table II. 

The Korwas are a Dravidian tribe living in Chuta Nagpur, in the districts of 
Sarguja, Jashpur, and Palamau, and claiming to be the aboriginal inhabitants. By 
some linguists the word Korwa is regarded as another form of Kol. They lead a 
nomadic life in the highlands, and armed with bows and arrows, are hunters and flesh 
eaters rather than agriculturists ; though to some extent they are cultivators, and clear 
the ground by burning the jungle. Dalton states that they are the most savage 
looking of the Kolarian group of tribes. They are strongly built and active ; the skin 
is dark brown, the face is broad, the forehead narrow, the hair is long and tangled, 
though in a figure of a man reproduced by Mr Crooke, the head is shaven ; they 
grow a beard and moustache. The more savage of the Korwas have black skins, 
flab faces, projecting chins, and tawny hair. In stature, the men of the Sarguja Korw&s 
averaged 5 feet 3 inches, the women 4 feet 9 inches ; but the men living on the Khiiria 
plateau were somewhat taller ; one measured 5 feet 8 inches. Both sexes are scantily 
clothed. They worship the tribal god Raja Chandol, and offer sacrifices to it, but the 
Sarguja tribe sacrifice to the spirits of their ancestors. They are totemistic, and 
apparently marriage is prohibited within the sept using the same totem. Mr Crooke 



74 PROFESSOR SIR W. TURNER ON 

says the marriage age for boys is twelve and ten for girls ; widows may remarry. 
Some families cremate, others bury the dead. Mr O'Donnell, in his Eeport on the 
Census of the Lower Provinces of Bengal, gives 79,954 persons as speaking the Korwa 
dialect of the Kolarian group of languages. 

The Indian Museum contains a skull (No. 404) of a man of the Korwa tribe, 
28 years old, named Fukeera, from Sargiija, Chiita Nagpiir. He died in prison, and 
the skull was presented by Lieut. -Colonel Dalton. 

The cranium in the norma verticalis was an elongated ovoid, very narrow, some- 
what roof-like in the sagittal region, and with the sides of the skull almost vertical. 
The length-breadth index was only 68 "8, and the skull was hyper-dolichocephalic. The 
parietal longitudinal arc was more than the frontal and much longer than the occipital. 
The basi-bregmatic height materially exceeded the greatest breadth, and the vertical 
index was 73*7. The parieto-occipital region sloped gently downwards, and the occipital 
squama was rounded and projected behind the inion. The glabella was moderate and 
the forehead was somewhat retreating. The nasion was shallow ; the bridge of the 
nose was slightly projecting and vertically concave. The nasal spine of the superior 
maxillae was distinct, and a sharp border separated the floor of the nose from the 
incisive region of the upper jaw. The nasal index was 5 8 '7, distinctly platyrhine ; the 
gnathic index, 94*3, was that of an orthognathous jaw. The orbital index, 71'8, was 
mesoseme, and the palato-maxillary index, 120, was brachyuranic. The complete 
facial index, 84, placed it in the low-faced group, chamseprosopic. The teeth were 
fully erupted, but not much worn ; the canine fossae were depressed. Small Wormian 
bones were in the lambdoidal suture. The skull was phsenozygous, and rested behind 
on the occipital bone. 

Munda, Ho, or Larkha Kol. Table III. 

The Miindas are a large non- Aryan tribe, occupying the plateau in Chuta Nagpiir 
which attains an elevation of 3000 feet. On linguistic grounds they are classed as 
Kolarian. Mr Bisley states that the name Miinda is of Sanskrit origin, and is applied 
to the headman of the tribe or village ; it is also used generally as a tribal name. As 
regards their language, physical characteristics, and customs, the Mundas, Hos, Bhiimij , 
Korwa, Kharrias and Santals are closely allied, and from speaking the languages of 
the Kolarian group, they are frequently classed together as Kols or Coles. There is a 
difference of opinion as to the derivation and meaning of the term Kol. It has been 
regarded as signifying pig, and used by the Indo-Aryans as a term of contempt applied 
to the aborigines ; but it is now, on the authority of Dalton, considered to be derived 
from the Mundari word Ho, or Horo, which means a man. According to tradition, the 
Kols were the earliest settlers in the valley of the Ganges. 

Dalton iu his account of the Mundas regards the Hos or Larkha (fighting) Kols as 
so closely allied to them, that they are often included together in the same descriptive 
sentence. He states that the Mundas are located in Singbhiim, Chuta Nagpiir, and in the 



CRANIOLOGY OF PEOPLE OF INDIA. 75 

territory known as Kolhan. The Hos admit that they are of the same family as the 
Miindas, and that they came from Chiita Nagpur. Dalton considers that from their 
isolation and independence, they furnish the best illustration of the characteristics of 
the Mundaris. They are physically a much finer people than the Bhiimij, Santals, or 
Kharrias. The men are 5 feet 5 or 6 inches in height, the women 5 feet 2 inches ; they 
have an erect carriage. The skin has a brownish coppery tint ; the eyes are dark 
brown; the hair is black, straight or wavy. Many have high noses, oval faces, and 
young girls are sometimes seen with delicate features, finely chiselled straight noses, so 
that there may be an admixture of Aryan blood. Dalton has also met some with 
strongly marked Mongolian features and a dark skin like the Santals. 

The clothing is reduced to a minimum, and often consists only of a loin-cloth 
brought between the thighs and fastened in front to a girdle. The women wear the 
hair collected into a kuot touching the back of the right ear and decorated with flowers. 
Marriage is between adults and is exogamous, and widow marriage is permitted. The 
national emblem is a godna or arrow. The dead are cremated and the ashes are buried, 
the spot being marked by a large grave-stone, and often a megalithic monument is set 
up outside the village. They are active and courageous, truthful and sensitive to 
wrong. They cultivate the ground, but eat also fowls and the flesh of pigs. They 
worship the sun and several other deities. In the general Report on the Census of 
1891, it is stated that the Miinda, Ho, Kol, Kur, and. Korwa people number 1,109,157 
by tribe, and that of these 840,282 speak the tribal language. 

In the series of skulls lent to me by the Indian Museum, six specimens are 
marked Kol or Cole. One of these, No. 31, from Singbhum, designated Larkha Kol, 
was presented by Colonel Dalton; another, No. 557, from the Kandhmals, marked 
Pan Cole, said to be 42 years old, height 5 feet 8 inches, and of dark complexion, was 
presented by Dr W. B. Stewart. Nos. 440, 442, and 444, also presented by Dr 
Stewart, were from Keunjhar, Orissa. No. 24, named Phugooa, given by Colonel 
Dalton, was from Moorgoo, Chiita Nagpur ; the age was said to be 65, the stature 
5 feet 5 inches ; hair of head straight, grey, that of face scanty ; eyes regular ; food 
rice, flesh, and vegetables. 

In the same museum were nine skulls, marked Munda from Chiita Nagpur. 
Of these, No. 25 is said to have been in height 5 feet 4 inches ; hair black, coarse, 
straight; eyes large, black, straight; food, rice, flesh, vegetables; whilst No. 26 was 34 
years old ; height 5 feet 5 inches ; hair black, coarse ; eyes large, black, straight ; food as 
above ; they were presented by Colonel Dalton. The others were collected in or near 
Kanchi by Mr W. H. P. Driver. Dr Hedley Wood has presented to me the skull of 
a woman aged 24, also obtained at Ranchi. 

Sixteen crania marked Munda or Kol have therefore come under observation ; 
thirteen of which are apparently those of men and three those of women. They are 
all adults, with the exception of No. 25, said to be that of a youth of 18, in which, 
though the wisdom teeth were not erupted, the basi-cranial synchondrosis was ossified. 
VOL. XL. PART I. (NO. 6). M 



PROFESSOR SIR W. TURNER ON 



Table III. 
Mtinda, Kol. 





o5 


rt 




S> 












Kol. 


Lark ha 
Kol. 


Kol. 






oJ 




"3 


TS 


o 


J5 


»*2 


• 8-L 


. •£ 


c5 a. 


rt 










. bo 




S 4> 

.2 d 


e 

-3 

§"8 




a r- 


a 


St 


as tc 




3 

-3 
3 












S p 


(S d 




S 










lis 


3 e3 


2-* 
■S.-S 


Mangr 
Ranch 
Old T( 


cS 3 


t8 

ir: 3 
"» 

►3W 


-3 S 

■« 


03 W 


Phugo 
Moorg 


1)2 

a 

OS 3 


Keunjhar. 




.5 % 




















Metopic. 


















I.M. 


I.M. 


I.M. 


I.M. * 


I.M. 


I.M. 


I.M. 


I.M. 


E.U.A.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. * 


Collection number, , 


25 


26 


603 


605 


606 


612 


607 


611 




24 


31 


440 


442 


444 


557 


604 


Age, . 


18 


32 


45 


Ad. 


Ad. 


Ad. 


Ad. 


Ad. 


24 


Ad. 


Adult. 


Aged. 


Adult. 


Adult. 


42 


Ad. 


Sex, . 


M. 


M. 


M. 


M. 


M. 


M. 


F. 


F. 


F. 


M. 


M. 


M. 


M. 


M. 


M. 


M. 


Cubic capacity, 


1248 


1210 


1375 


1430 


1315 


1310 


1000 


1110 


1180 


1306 


1215 


1470 


1176 


1220 


1388 


1200 


Glabello-occipital length 


176 


179 


180 


191 


183 


180 


165 


168 


170 


182 


175 


182 


176 


178 


191 


164 


Basi-bregmatic height, 


132 


128 


131 


141 


133 


129 


130 


126 


128 


130 


130 


138 


130 


130 


126 


132 


Vertical Index, 


75- 


71'5 


72'8 


73-8 


72'7 


71-7 


75-5 


76' 


75'3 


71'4 


74'3 


75'8 


73-9 


73' 


66' 


80S 


Minimum frontal dia 


































meter, 


89 


89 


96 


97 


89 


90 


88 


92 


91 


94 


90 


101 


94 


95 


97 


93 


Stephanie, 


102 


105 


102 


109 


99 


100 


89 


97 


109 


111 


110 


121 


107 


110 


118 


107 


Asterionic, 


105 


100 


104 


109 


99 


105 


89 


93 


102 


104 


106 


106 


101 


104 


110 


99 


Greatest parieto-squam 


































ous breadth, 


123s. 


127s. 


134s. 


130s. 


131p. 


129p. 


112s. 


122s. 


125 


132s. 


132s. 


137s. 


127s. 


127s. 


141s. 


132s. 


CepJudic Index, 


69-9 


70'9 


W4 


68-1 


71'6 


71-7 


68' 


72-6 


73'5 


72'5 


75 '4 


75'3 


72-2 


71'3 


73-8 


80-5 


Horizontal circumference 


, 488 


491 


493 


521 


498 


491 


448 


460 


480 


506 


492 


515 


495 


497 


534 


470 


Frontal longitudinal arc 


125 


112 


124 


135 


124 


120 


112 


116 


120 


130 


122 


130 


122 


124 


130 


118 


Parietal , , , , 


131 


125 


124 


133 


{257 


136 


120 


130 


127 


129 


121 


132 


130 


136 


113 


117 


Occipital ,, ,, 


111 


118 


112 


130 


110 


103 


99 


101 


112 


116 


120 


108 


104 


128 


108 


Total ,, ,, 


367 


355 


360 


398 


381 


366 


335 


345 


348 


371 


359 


382 


360 


364 


371 


343 


Vertical transverse arc, 


278 


285 


301 


312 


287 


291 


277 


280 


237 


298 


290 


312 


287 


295 


298 


300 


Length of foramen mag 


































num, . 


35 


35 


33 


31 


36 


32 


31 


32 


32 


35 


31 


34 


31 


33 


34 


33 


Basi-nasal length, . 


91 


101 


101 


102 


94 


96 


98 


93 


95 


98 


95 


101 


101 


101 


101 


97 


Basi-alveolar length, 


88 


95 


93 


102 


93 


96 


95 


88 


94 


93 


86 


100 


99 


• ■• 


99 


95 


Gnathic Index, 


96-7 


94'1 


92'1 


100' 


98-9 


100- 


96 '9 


94-6 


98'9 


94'9 


90-5 


99' 


98' 


■ *• 


98' 


97'9 


Interzygomatic breadth, 


. 123 


122 


128 


130 


131 


128 


115 


120 


125 


125 


131 


133 


... 


... 


133 


126 


Interinalar ,, 


. 112 


109 


118 


122 


120 


118 


109 


110 


114 


104 


119 


120 






120 


115 


Nasio-mental length, 


. 102 


107 


115 


117 


106 


103 


98 




.* • 




107 










100 


Nasio-alveolar ,, 


59 


62 


62 


70 


60 




54 


56 


64 


60 


63 


68 


63 




63 


58 


Complete Facial Index, 


82-9 


87'7 


89'8 


90. 


80-9 


80 -4 


85'2 


... 




... 


81'6 












Nasal height, . 


45 


47 


47 


52 


48 


45 


41 


42 


47 


46 


50 


54 


48 




47 


43 


Nasal width, . 


23 


26 


23 


27 


25 


25 


24 


22 


25 


23 


26 


25 


22 




27 


24 


Nasal Index, . 


51-1 


55'3 


48-9 


51'9 


52-1 


55- 5 


58-5 


52'4 


53-2 


50' 


52' 


46-3 


45-8 


• t • 


57 '4 


55'8 


Orbital width, 


35 


39 


39 


40 


37 


36 


37 


37 


36 


37 


40 


40 


39 


• •• 


40 


38 


Orbital height, 


34 


31 


30 


30 


29 


31 


30 


34 


33 


32 


32 


33 


34 


... 


30 


30 


Orhital Index, 


97-1 


79-5 


76-9 


75' 


78-4 


86'1 


si-i 


91'9 


91-7 


86-5 


80' 


82-5 


87'2 


... 


75' 


78-9 


Palato-maxillary length 


49 


53 


49 


58 


56 


... 


51 


45 


50 


54 


47 


60 


55 


• •a 


53 


51 


Palato-maxillary breadth 


, 62 


66 


63 


68 


64 




62 


• «• 


60 


64 


66 


69 


65 




63 


59 


Palato-maxillary Index, 


126' 


124' 


128S 


117'2 


114-2 




121-5 


,, , 


120' 


118' 


140' 


115' 


118' 


... 


118- 


115-6 


( Symphysial height, 


30 


29 


31 


32 


31 




27 


... 


..* 




30 




• • • 


... 




26 




Coronoid ,, 


60 


62 


65 


66 




63 


53 




.. • 




66 






... 




52 


•„■ 


Condyloid ,, 


60 


60 


63 


64 


• •• 


59 


54 


... 


... 


... 


61 


... 








58 


.2, 


Gonio - symphysia 


I 
































t- 
o 


length, 


85 


86 


86 


91 


86 


88 


80 




■ ■• 


... 


85 


• ■ * 






... 


80 




Inter -gonial width 


































3 


outside, 
Breadth of ascending 


85 

1 


91 


95 


99 


92 


93 


93 




... 


... 


91 




... 






86 




,. ramus, 


30 


30 


37 


35 


35 


31 


33 








32 






... 




35 



With Skeletons. 



CRANIOLOGY OF PEOPLE OF INDIA. 77 

Of the sixteen crania, No. 604, stated in the museum list to be Jattia Munda, of 
Bhowro village, near Ranchi, differed so greatly in the form and proportions of the 
cranium from the others, that it will be described in a separate paragraph (p. 79). The 
following description applies therefore to fifteen skulls, and of these No. 444 consisted 
only of the calvaria. The lower jaw was absent in several specimens. 

The crania presented in the norma verticalis an elongated ovoid form, with steep 
sides and moderate parietal eminences. The sagittal region showed no special ridge or 
flattening, nor was the slope outwards to the parietal eminence, though distinct, so 
marked as one sees in some aborigines. In the males, the glabello-occipital length ranged 
from 165 to 191 mm., and the greatest breadth from 123 to 141 mm. In three crania 
the cephalic index was below 70, hyper-dolichocephalic ; in ten it ranged from 70 to 75, 
dolichocephalic ; in two it was between 75 and 76, essentially dolichocephalic, though 
numerically in the mesaticephalic group. The mean cephalic index of the fifteen crania 
was 72. In these skulls the occipital was the smallest of the three longitudinal arcs, 
except in one specimen where it exceeded the frontal ; usually the parietal had the 
longest arc, but in five specimens the frontal was the longer. In the males, the basi- 
bregmatic height ranged from 126 to 141 mm. ; in the females from 126 to 130 mm. 
The mean vertical index in the fifteen crania was 7 3 '4, i.e., metriocephalic. The basi- 
bregmatic height exceeded the greatest breadth in ten skulls ; in four it was less, and in 
two the diameters were equal. 

The forehead in the men did not much recede, and the skull sloped gently 
backwards in the parieto -occipital region ; as a rule, the occipital squama was rounded, 
and projected behind the inion. The glabella and supra-orbital ridges were moderate ; 
as a rule the nasion was not depressed. The nasal bones were not large, and the bridge 
was either feeble or only moderately projected. The nasal spine of the superior maxillae 
was moderate. In some specimens a ridge demarcated the floor of the nose from the incisive 
region ; but as a rule, they rounded off into each other. The mean nasal index in 
fourteen skulls was 52'1, high in the mesorhine series; but in the individual specimens, 
whilst five were markedly platyrhine, seven were mesorhine, and two were leptorhine ; 
eight skulls were microseme, and the mean orbital index of the series was 83 '5, i.e., 
microseme ; but the range of variation was considerable, so that three were in the 
megaseme group and three were mesoseme. The mean gnathic index of the series was 
96*6, i.e., orthognathous ; no specimen was prognathous, and only six were mesogna- 
thous. In the male skulls the greatest interzygomatic breadth was 133 mm., but the 
mean often specimens was only 128 '4, which is materially below the measurements of 
the face breadth given in Part I. of this memoir, in the Chinese, Burmese, Nagas, and 
Esquimaux. Owing to the lower jaw being absent in several specimens, the nasio- 
mental diameter could only be taken in eight skulls, all of which were chamseprosopic, 
and the mean of the series was 84*8. The mean palato-maxillary index was brachy- 
uranic, 12T7, and only one skull was below the lowest term of that group. 

One skull, that of a woman, was metopic. The sutures were as a rule distinct. 



78 



PROFESSOR SIR W. TURNER ON 



though in some they were more or less obliterated. The skull marked Pan Cole 
had a transverse depression behind the coronal suture as if from wearing a band 
during infancy. Wormian bones were present in the lambdoidal suture in several 
specimens. Three crania had a single epipteric bone, and in No. 25 the squamous tem- 
poral articulated with the frontal ; no skull had a third condyle, but in No. 557 each 
occipital condyle was divided into an anterior and a posterior facet. The jugal 
processes were sometimes tuberculated. The crania rested behind either on the mas- 
toids or occipital region. Several specimens showed the infra-orbital suture, and in one 
of these the superior maxilla and sphenoid articulated at the anterior end of the spheno- 
maxillary fissure. The cranial capacity ranged in twelve men from 1176 to 1470 c.c. ; the 
mean of the series was 1305 c.c, and seven specimens exceeded the mean. In the 
three women the range was from 1000 to 1180, and the mean was 1097 c.c. 

No. 605, Biphaiya Miinda from Madkom village, near Ranchi, was accompanied 
by a skeleton, the bones of which I have examined. 

Pelvis. — The chief measurements of the pelvis are given below. The alse 
were expanded and the iliac fossa were not translucent ; the subpubic angle was 
relatively wide ; the pectineal lines were not knife-like ; there was a shallow preauricular 
sulcus. The breadth-height index of the entire pelvis was 81 "2. The transverse 
diameter of the brim was much more than the conjugate, and the brim index was 
86' 7, i.e., platypellic* The sacrum consisted of five vertebrae, and the sacral index 
was 110*5, i.e., platyhieric. 

Measurements of Pelvis. 



Collection, Indian Museum, . 


No. 605 


No. 604 










Sex, ..... 




M. 


M. 










1. Breadth of pelvis, 




245mm 


246mm 










2. Height of pelvis, . 




199 


178 










3. Breadth-height Index, . 




81-2 


72-3 










4. Between ant. sup. iliac spines, 




215 


222 










5. Between post. sup. iliac spines, 




82 


73 










6. Between ischial tubera, . 




136 


116 










7. Vertical diameter of obturator foramen, . 


45 


48 










8. Transverse diameter of obturator foramen, 


33 


29 










9. Obturator Index, ..... 


73-3 


60-4 










10. Subpubic angle, .... 




83° 


62* 










11. Transverse diameter of brim, . 




113 


114 










12. Conjugate diameter of brim, . 




98 


87 










13. Pelvic Index, 




86-7 


76-2 










14. Length of sacrum, 




95 


4 vert. 










15. Breadth of sacrum, 




105 


102 










16. Sacral Index, 




1105 


... 











True Vertebrae. — The cervical vertebras were normal. Of the twelve dorsal vertebras 
1st to 8th were normal. The 9th had a small costal articular facet at the upper border, 
but none at the lower border of the side of the body. The 10th, 11th, and 12th had 

* For the meaning of this and several other descriptive terms used to denote proportion between certain diameters 
of the skeleton, see my Report on Human Skeletons, in Challenger Reports, Part XLVIL, 1886. 



CRANIOLOGY OF PEOPLE OF INDIA. 



79 



each a large single costal facet at the side of the body. The transverse process of 
the 10th dorsal had no costal facet, and those of the 11th and 12th had the usual 
three tubercles. The lumbar vertebrae were of the customary shape. The vertical 
diameter of their bodies in front and behind was as follows : — 





A.V.D. 


P.V.D. 


Indices. 


1st lumbar, 


24 mm. 


25 mm. 


104 


2nd „ 


23 „ 


26 „ 


113 


3rd „ 


23 „ 


26 „ 


113 


4th „ 


20 „ 


22 „ 


110 


5th „ 


21 „ 


21 „ 


100 



Total 111 mm. Total 120 mm. Mean 108-1 

In this skeleton the upper four vertebrae had the posterior vertical diameter longer 
than the anterior. It is customary to find the antero-vertical diameter of the 5th 
vertebra longer than the postero-vertical, but in this specimen they were equal. The 
mean general index of the series of five vertebrae was as high as 108*1, which places 
the lumbar spine in the koilorachic group. 

Upper Limb. — Clavicles slender, right 138 mm., left 136 mm. long; subclavian 
groove shallow. Scapulae: right, 143 mm. long, 105 broad, index 73*4; left, 150 
mm. long, 106 broad, index 70*6. Supra-scapular notch shallow and wide, but with 
a distinct border. Humerus with shallow musculo-spiral groove and moderate 
muscular impressions, no supra-condylar process or inter-condylar foramen. Bones of 
forearm not specially noticeable. Radio-humeral index, 83*3 or dolichokerkic. 



Right. 
307 mm. 
256 „ 
252 „ 
281 „ 
276 „ 



Left. 

312 mm. 

255 „ 

250 „ 

281 „ 

278 „ 



Humerus, head to trochlea, 
Radius to tip of styloid, . 

„ base „ 
Ulna to tip of styloid, 
„ articular surface, . 

Lower Limb. — Femur with linea aspera and external condylar ridge fairly well 
marked, also the trochanters and gluteal ridge ; no platymery ; articular area on 
internal condyle prolonged forwards and lying in the same transverse plane as the 
origin of the inner head of the gastrocnemius ; popliteal surface plano-concave. 
Tibia with the head retroverted ; condylar surfaces with shallow concavities ; antero- 
posterior diameter of shaft of right tibia in plane of nutrient foramen, 36 mm. ; 
transverse diameter in same plane 25 mm. ; index of platyknemia 6 9 "4 ; the corre- 
sponding diameters of the left bone were 37 and 24 mm. No articular facet on the front 
of lower end of left tibia continuous with the astragalar area was seen, but a slight 
indication of one was present in the right bone. The fibulae had strong oblique ridges 
and a deep concavity for the origin of the tibialis posticus. 

No. 604, referred to on p. 77, and marked Jattia Miinda from Bhowro village, is so 
different in configuration from the other Miinda crania that there can, I think, be little 
doubt that it has been erroneously named by the collector. The skull is brachycephalic, 
80'5, in its proportions and form. It was rounded in outline when seen from the 



80 PROFESSOR SIR W. TURNER ON 

norma verticalis, and comparatively flattened on the vertex. The frontal and parietal 
eminences were distinct, and the skull sloped steeply downwards in the parieto-occipital 
region, where it was unsymmetrical and flattened on the left side. The frontal 
longitudinal arc was the longest ; the basi-bregmatic diameter was the same as the 
parieto-squamous. The upper jaw was orthognathous, the nasal index was platyrhine, 
the orbital index was microseme, and the palato-maxillary index was barely brachy- 
uranic. Although I have given the measurements of the lower jaw sent with the skull, 
I doubt if it really belonged to it. The cranial capacity was 1200 c.c. 

The skull was accompanied by other bones of the skeleton. 

Pelvis. — The measurements of the pelvis are given on page 78. The iliac fossas 
were translucent, and the alas were expanded ; the subpubic angle was acute ; the 
obturator foramen had a long vertical diameter. The pelvis was broad in relation to 
the height, and the index was 72 '3. The transverse diameter of the pelvic brim 
greatly exceeded the conjugate, and the brim index, 76 - 2, was platypellic. The 
pectineal lines were knife-like ; the preauricular sulcus was faintly marked. Only four 
sacral vertebras were present ; the body of the 4th was oval like a normal 5th, and its 
laminas formed two sacral cornua and did not meet behind in a spine. The base of the 
sacrum had on the right of its body an articular surface for the right transverse process 
of the 5th lumbar vertebra. 

True Vertebras. — The cervical vertebras were normal. The dorsi-lumbar vertebrae 
were eighteen in number. The 10th had a single facet on the side of the body for a part 
of the head of the 10th rib ; the 11th and 12th had single facets for their corresponding 
ribs, they had both rudimentary transverse processes, and the inferior articular processes 
of the 12th dorsal were convex, and looked forwards and outwards. There were six 
vertebras between the 12th dorsal and 1st sacral. The first of these approximated in 
shape to the 12th dorsal; its transverse processes were rudimentary, and showed the 
superior, inferior and external tubercles. On the side of the pedicle, immediately in front 
of the external tubercle, was a smooth facet 2 mm. in diameter, apparently for the head 
of a rudimentary rib ; its articular processes had the characters of a lumbar vertebra. 
The remaining five vertebras had the customary lumbar characters, and the right 
transverse process of the lowest was divided by a deep furrow into a non-articular part, 
and an articular part which was jointed to the base of the sacrum. The vertical 
diameters of the bodies of these vertebras, in front and behind, was as follows : — 





Ant. V. Diam. 


Post. V. Diam. 


Index. 


Dorsi-lumbar, 


23 mm. 


26 mm. 


113 


1st lumbar, . 


24 „ 


26 „ 


108-3 


2nd „ . 


24 „ 


25 „ 


104-1 


3rd „ . 


23 „ 


24 „ 


104-3 


4th „ . 


22 „ 


22 „ 


100- 


5th „ 


24 


21 


87-5 




Total 117 mm. 


Total 118 mm. 


Mean 100-8 



CRANIOLOGY OF PEOPLE OF INDIA. 



81 



In this skeleton the 4th lumbar body showed an equality in the vertical diameters ; 
in those higher up the posterior diameter exceeded the anterior, whilst in the lowest, 
the anterior was distinctly greater than the posterior diameter. The mean general 
index of the series of five vertebras was 100*8, and the lumbar spine was in the 
orthorachic group. 

Upper Limb. — The bones of the upper limb were slender, and the muscular 
markings were feeble. The Humerus had neither supra-condyloid process nor inter- 
condylar foramen ; the musculo-spiral groove was shallow, and the shaft had only a 
slight twist. The right radio-humeral index was 75"3, mesatikerkic. 





Right. 


Left. 


Humerus, head to trochlea, 


292 mm. 


288 mm 


Radius, head to tip of styloid, 


220 „ 


222 „ 


,, ,, base „ ... 


217 „ 


216 „ 


Ulna, olecranon to tip of styloid, . 


238 


240 „ 


„ „ lower articular surface, . 


234 

-jut ,, 


236 „ 



The Clavicles were : right bone, 129 mm., left, 134 mm. long ; their subclavian 
grooves were scarcely marked. The right Scapula was 129 mm. long and 91 broad, 
index 70*5 ; the left was 129 mm. and 94 broad, index 72*9; the supra-scapular notch 
was shallow and not differentiated from the superior border by a sharp margin. 

Lower Limb. — The bones of the lower limb were also slender. In the Femur the 
trochanters and gluteal ridges were fairly marked, but there was no platymery. The 
linea aspera and external condylar ridge were distinct, the popliteal triangle was flattened 
or faintly concave ; the inner condylar articular surface was prolonged backwards and in 
the same transverse plane as the place of origin of the inner head of the gastrocnemius. 
The head of the Tibia was slightly retroverted ; the lower articular end was not prolonged 
on the front of the bone. The antero-posterior diameter of the shaft in the plane of 
the nutrient foramen was for the right bone, 28 mm. ; for the left, 27 mm. ; the 
transverse diameter was in each bone 21 mm. ; the index of platyknemia was 75 in 
the light tibia. 

In No. 605 the tibio-femoral index 86 '4 was dolichoknemic ; in No. 604 the index 
was 82*96, practically also dolichoknemic, i.e., with a relatively long tibia. 



No. 604. 



No. 605. 



Femur, maximum length, 

„ oblique length, 
Tibia, condylar surface to tip of malleolus, 

>j „ „ astragalar surfacp, 

Fibula, maximum length, 



Right. 


Left. 


Right. 


Left. 


410 mm. 


410 mm. 


445 mm. 


445 mm 


405 „ 


408 „ 


441 „ 


441 „ 


343 „ 


336 „ 


395 „ 


393 „ 


336 „ 


332 „ 


381 „ 


381 „ 


341 „ 


339 „ 


377 „ 


378. „ 



82 PROFESSOR SIR W. TURNER ON 



Bhumij. Table IV. 



The Bhumij is a non- Aryan tribe living in the Manbhiim and Singbhum districts of 
Chiita Nagpur as well as in Western Bengal. They are regarded as the original inhabi- 
tants, and are located by Dalton in the country between the Kasai and Subarnarekha 
rivers. They have been classed on linguistic grounds as Kolarian ; most authorities 
regard them as closely allied to, and probably identical with, the Miindas, with whom 
they associate and intermarry. Dalton says that their appearance is inferior to that of 
the best of the Miindas and to the Hos of Singbhum. They are short, but strongly 
built. The skin ranges in colour from a light brown to a dark chocolate. They build 
commodious houses and practise adult marriage. The divisions of the tribe are totem- 
istic, and the marriage of adults is exogamous, as amongst the Miindas ; widows may 
remarry. The dead are cremated, and the body is laid upon the pyre with the head to 
the south ; the ashes are buried under gravestones, which are sometimes of large size. 
They are agriculturists, but they eat fowls and drink fermented liquors. They worship 
the sun as well as minor deities. Their numbers do not appear to have been separately 
recorded in the General Report on the Census of 1891, but in the special census of the 
lower provinces of Bengal and their Feudatories, Mr C. J. O'Donnell gives a total of 
306,473. 

I have examined two skulls of the Bhiimij tribe, both adult males, collected at Man- 
bhum. One in the Indian Museum, No. 18, is named Aunundo Bhoomiz ; in the list 
supplied to me he is said to have been 40 years of age, 5 feet 3 inches in height, hair and 
eyes black, whiskers small. The other, a male named Karnai, aged 30, was presented 
to me by Dr J. J. Hedley Wood. 

In both specimens the cranium was long, relatively narrow, and roof-shaped in the 
sagitto-parietal region. The parietal eminences were well in front of the occipital point 
which projected behind the inion ; the side walls of the cranium were almost vertical. 
In one skull the length-breadth index was 727, in the other 70'9 ; both were dolicho- 
cephalic. In one the frontal and parietal longitudinal arcs were equal and in excess of 
the occipital ; in the other the frontal arc was the longest. In one the basi-bregmatic 
diameter was less than the greatest breadth ; in the other it was slightly longer. The 
glabella and supra-orbital ridges were moderately projecting ; the forehead slightly 
receded ; the antero-posterior curve of the vault rose gradually to the vertex, and then 
sloped gently downwards to the occipital squama. In neither skull was any sign of 
parieto-occipital flattening. The nasion was somewhat depressed ; the nasal bones were 
short, concave forwards, and orAy feebly projecting. The nasal spine of the superior 
maxillae was moderate, and the floor of the nose was separated by a slight ridge from the 
incisive surface of the jaw. 

The nasal index in both specimens was in the higher mesorhine group ; the gnathic 
index in both was orthognathons ; one skull was mesoseme, the other megaseme ; the 



CRANIOLOGY OF PEOPLE OF INDIA. 



83 



Table IV. 
Bhumij and Tun Races. 





BMmij. Manbhum. 






Turi. 














Manbhum. 




















Race 




















unknown. 
















Aunundo 
Bhoomiz. 


Karnai. 


Scapho- 
cephaly. 




Bitna. 
Surungee. 


Sookeam. 
Teerrah. 










I.M. 


E.U.A.M. 


I.M. 




I.M. 


I.M. 








Collection number, 


18 




407 




22 


23 








Age 


40 


30 


Ad. 




28 


35 








Sex, ..... 


M. 


M. 


M. 




M. 


M. 








Cubic capacity, 


1414 


1235 


1410 




1280 


1435 








Glabello -occipital length, 


183 


182 


194 




183 


188 








Basi-bregmatic height, . 


131 


130 


137 




132 


132 








Vertical Index, 


71-6 


71-4 


70-6 




72-1 


70-2 








Minimum frontal diameter, 


94 


89 


93 




93 


95 








Stephanie, .... 


115 


113 


107 




110 


111 








Asterionic, .... 


105 


100 


114 




99 


109 








Greatest parieto-squamous 




















breadth, .... 


133s. 


129 


125s. 




133p. 


135s. 








Cephalic Index, 


72-7 


70-9 


64-4 




72-7 


71-8 








Horizontal circumference, 


517 


502 


520 




514 


518 








Frontal longitudinal arc, 


135 


130 


137 




128 


127 








Parietal „ „ 


135 


125 


143 




131 


118 








Occipital „ „ 


114 


103 


124 




106 


129 








Total ,, ,, 


384 


363 


404 




365 


374 








Vertical transverse arc, . 


302 


233 


298 




30S 


304 








Length of foramen magnum, . 


36 


34 


32 






38 








Basi-nasal length, . 


95 


101 


102 




101 


99 








Basi-alveolar length, 


92 


93 


94 




102 


101 








Gnathic Index, 


96-8 


92-1 


92-2 




101 


102 








Interzygomatic breadth, . 


129 


126 


125 




124 


134 








Intermalar „ 


110 


119 


117 




115 


121 








Nasio-mental length, 


120 


113 


109 


i 


110 








Xasio-alveolar „ 


66 


64 


65 




61 


66 








Complete Facial Index, . 


93 


89 7 








82 








Nasal height, 


50 


46 


48 




44 


46 








Nasal width, 


26 


24 


24 




27 


24 








Nasal Index, 


52 


52-2 


50 




61-4 


52-2 








Orbital width, 


38 


35 


37 




41 


39 








Orbital height, 


33 


32 


29 




31 


30 








Orbital Index, 


86-8 


91-lf 


78-4 




75-6 


76-9 








Palato-maxillary length, 


53 


52 


52 




56 


58 








Palato-maxillary breadth, 


61 


69 


61 




65 


65 








Palato-maxillary Index, 


115 


132-7 


117-3 




116- 


112- 










' Symphysial height, 


35 


32 


29 






32 








g- 


Coronoid „ 


65 


55 


64 






64 










Coudyloid „ 


58 


59 


65 






65 








<0 


Gonio-symphysial length, 


91 


82 


89 






96 








ft 


Inter-gonial width outside, 


96 


95 


96 






98 








H? 


Breadth of ascending 






















ramus, 


30 


33 


37 






38 









VOL. XL. PART I. (NO. 6). 



N 



84 PROFESSOR SIR W. TURNER ON 

palatomaxillary index in one was brachyuranic, in the other mesuranic. In one 
the complete facial index was chamseprosopic, in the other high-faced leptoprosopic. 
The teeth were somewhat worn from use ; the canine and incisor fossae were deep. 
The cranial sutures were distinct. In one there were no irregular ossifications ; in 
the other the right pterion had a large epipteric bone. The muscular ridges and 
processes were well marked. In one the cubic capacity, 1414, was mesocephalic ; 
in the other, 1235 c.c, microcephalic. The lower jaw was well proportioned and 
possessed a square chin. 

Another skull from Manbhum, an adult male, No. 407 in the Indian Museum, is 
marked " race unknown." It is a characteristic specimen of a scaphocephaly cranium. 
Although not known to be a Bhiimij, yet as it came from Manbhum, it is convenient to 
describe its characters here. The skull was greatly elongated and narrow, strongly 
keeled in the sagittal region, and with the suture obliterated ; the lambdoidal suture 
was almost completely obliterated, but the coronal and the lateral longitudinal sutures 
were to all appearance unossified. The glabella and supra-orbital ridges were prominent, 
and the nasion was depressed. The nasal bones were short and prominent. The canine 
and incisive fossae were deep. The nasal spine of the superior maxillae was moderate. 
The dimensions of the skull are given in Table IV. The modifications in shape produced 
by the premature closure of the sagittal and lambdoidal sutures have, however, deprived 
this skull of any ethnic significance. It will be seen from the Table that owing to the 
elongation of the cranium and the diminished parieto-squamous breadth, the length- 
breadth index is only 64*4. The cubic capacity, 1410 c.c, is apparently not affected by 
the cranial deformity. 

Turi. Table IV. 

The Turis are a non- Aryan tribe or caste, living in Chiita Nagpiir. In his account of 
these people Mr Risley states that they are without doubt a Hinduised offshoot of the 
Miindas. He adduces in support of this opinion the following : — They use amongst 
themselves a dialect of Mundari ; their totems correspond closely with those in force 
amongst the Miindas ; their original religion is closely akin to the form of animism 
current among the Miindas. 

The Turis are cultivators and makers of baskets. They are, like the Miindas and 
Oraons, lax in articles of food. Each sub-caste is strictly endogamous. Girls usually 
marry as adults and widows can marry again. The caste is small, and in 1881 num- 
bered apparently about 30,000 persons. 

Two crania, marked Turi, are in the Indian Museum. No. 22 is that of Bitna, from 
Surungee. He was 28 years old ; 5 feet 4 inches high ; hair black, straight ; eyes black, 
small ; no beard or whiskers. No. 23, Sookeam, was from Teerrah. He was 35 years 
old ; 5 feet 3 inches high ; hair black, straight ; eyes black ; no beard or whiskers. Both 
men had been hanged in Ranchi jail as murderers. 



CRANIOLOGY OF PEOPLE OF INDIA. 85 

The skulls resembled each other in the norma verticalis ; they were elongated ovoids, 
with distinct parietal eminences, and with a moderate slope outwards from the sagittal 
suture. They were both dolichocephalic, the mean length -breadth index being 72*2 ; in 
Bitna the parietal arc was a little longer than the frontal, but in Sookeam the occipital 
arc had the unusual diameter, 129 mm., and was longer than either the frontal or 
parietal. In each skull the basi-bregmatic height was slightly less than the breadth. 
The forehead was moderately receding, and the glabella and supra-orbital ridges were not 
prominent ; the crania sloped gently backwards and downwards from the obelion ; the 
occipital squama was rounded and prominent. The upper jaw slightly projected, and 
the gnathic index, mesognathous, was 101 and 102. The nasion was shallow ; the 
bridge of the nose was concave vertically ; the nasal spine of the superior maxillae was 
moderate, and the anterior nares were rounded at the junction of the side-wall and floor. 
The nasal index in Bitna was markedly platyrhine ; in Sookeam it was mesorhine, and in 
his skull the face was chamseprosopic. In both skulls the orbital index was microseme ; 
in one the palato-maxillary index was mesuranic, in the other in the lower term of the 
brachuranic group. In No. 22 the arch of the palate was much deeper than in No. 23. 
Both crania were barely cryptozygous, and they rested behind on the cerebellar part 
of the occiput. In Bitna the wisdoms were erupted, in the other skull in process of 
eruption ; the incisor fossae were deeper than the canine. The frontal suture was closed, 
but the other sutures were not ossified. In No. 23, small Wormian bones were in the 
lambdoidal suture, but there were no other special abnormalities. The muscular ridges 
were fairly developed. In Bitna the cranial capacity was only 1280 c.c, i.e., micro- 
cephalic, whilst in Sookeam the capacity, 1435 c.c, placed it high in the mesocephalic 
group. 

Juang. Table V. 

The Juangs are a non-Aryan tribe living in the hill districts of Dhekanai and 
Keunjhar, two of the tributary states of Orissa. Dalton groups them with the 
Kolarians on account of some affinities of language, but he also says that, whilst they 
have adopted many Uriya words, they employ vocables which cannot be connected with 
any Aryan, Kolarian, or Dravidian language. They are a primitive people, and claim 
to be the autochthones in Keunjhar. They are remarkably shy and timid. The stature 
of the men is somewhat less than 5 feet, that of the women about 4 feet 8 inches ; the 
forehead is upright, but narrow and low ; nasal bones depressed, alse of nose spreading ; 
mouth large, lips thick, upper jaw rarely prognathous, chin receding ; hair coarse and 
frizzly ; prevailing colour of skin a reddish brown ; the jaw is flat, and the cheek bones 
are strongly projecting. The women tattoo the forehead and temples. Those seen by 
D alton were not clothed, but wore a girdle composed of several strings of beads from 
which depended scanty curtains of leaves. The men wear a small cotton loin cloth. 
They had no knowledge of metals or pottery. They cremate the dead, and place the 
body on the bier with the head to the south ; the ashes are thrown into a running 



86 PROFESSOR SIR W. TURNER ON 

stream. Their huts are low, and measure about 6 feet by 8 ; but the boys of the village 
occupy a common dormitory. Marriage takes place between adults, and widows may 
remarry. They are exogamous. They are semi-nomadic in their habits, cultivate the 
ground sparingly, and eat all kinds of flesh. Little is known of their religious creed, 
and they make sacrifices to the sun and earth. 11,171 persons were said in 1891 to 
speak the tribal language. 

The Indian Museum contains two skulls from Keunjhar in the Orissa hills, stated 
in the MS. Catalogue to be those of Juangs. They were presented by Dr Stewart in 
1868. The larger skull, No. 443, is that of a man. The smaller, No. 446, is that of 
a woman. The male skull in the norma verticalis was an elongated ovoid, sloping 
steeply from the sagittal suture to the parietal eminences, below which the side walls 
of the skull were almost vertical. The cephalic index was 73"2, and the skull was 
dolichocephalic in form and proportions. In both, the parietal longitudinal arc exceeded 
the frontal. The height in the male was greater than the breadth, and the vertical index 
was 79 "3. The glabella and supra-orbital ridges were moderate, the forehead was not 
specially receding, the slope from the obelion was not precipitous, and the occipital 
squama above the inion was not prominent, but there was no evidence of parieto-occipital 
flattening. The fronto-nasal suture was shallow ; the nasal bones were short, narrow, 
concave forwards, and only slightly projecting. The canine and incisor fossse were not 
specially marked ; the skull was barely cryptozygous, it rested behind on the mastoids. 
The occipital bone sloped steeply upwards from the foramen magnum to the inion. 
The muscular ridges and processes were moderate ; the sutures were simple and often 
with two small Wormian bones in the lambdoidal suture. The parieto-sphenoid articu- 
lations were broad. The sockets of the teeth were broken, and there were no marked 
osseous irregularities. 

The female skull was much smaller ; it was more flattened on the vertex than the 
male. Proportionally it was not so elongated, and its cephalic index was 77*4. The 
height was a little less than the breadth, and the vertical index was 76 '2. The fore- 
head was more vertical, and the glabella and supra-orbital ridges were feeble ; the 
occipital squama above the inion was more projecting, and below the inion it was not 
so steep as in the male skull. There was no evidence of parieto-occipital flattening. 
The nasal bones were larger than in the man, but the bridge of the nose had a similar 
curvature. The canine fossae were more hollowed out, and the teeth were much worn 
down. The cranial sutures were in process of obliteration ; small Wormian bones were 
present in the lambdoidal suture ; the parieto-sphenoid articulation was moderately 
broad. The mastoids were very feeble. The skull was cryptozygous, and rested behind 
on the occipital condyles. 

Both crania were orthognathous and platyrhine. The proportions of the orbit in 
the woman were microseme, and in the man megaseme. The cranial capacity of the 
woman was very low, 1030 c.c. ; but in the man it reached 1420 c.c. 



CRANIOLOGY OF PEOPLE OF INDIA 



87 



Table V. 



Juangs, and various Tribes or Castes. 

















Ahir- 


Teli. 


Kamar. 






Juang. 


Koydwar. 
Nagooloo. 


Bunjana. 


Bhirna. 


Goala. 
Teetoo. 






Bhudny. 
Hazari- 


Lohar. 
Ranchi. 


Pittoria 


Soromoo. 
















Puttea. 


Village. 


Raipur. 


bagh. 






I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


E.U.A.M. 


E.U.A.M. 


I.M. 


Collection number, . 


443 


445 


284 


285 


602 


599 


27 


598 






600 


Age, 


Ad. 


Ad. 


50 


40 


Ad. 


Ad. 


25 


Ad. 


23 


Ad. 


Ad. 


Sex, 


M. 


F. 


M. 


M. 


M. 


F. 


M. 


M. 


F. 


F. 


F. 


Cubic capacity, 


1420 


1030 


1267 


1292 


1270 


1170 


1328 


1370 


1005 


1230 


1240 


Glabello-occipital length, . 


179 


164 


181 


166 


180 


178 


183 


184 


168 


173 


170 


Basi-bregmatic height, 


142 


125 


126 


131 


132 


125 


135 


138 


110 


128 


131 


Vertical Index, 


79S 


76-2 


69-6 


78-9 


73-3 


70-2 


73-8 


75- 


65-8 


74- 


77-1 


Minimum frontal diameter, 


95 


87 


87 


93 


89 


92 


89 


95 


89 


90 


90 


Stephanie, .... 


109 


110 


112 


112 


102 


103 


102 


109 


104 


102 


107 


Asterionic, .... 


103 


94 


104 


106 


100 


98 


100 


108 


94 


100 


103 


Greatest parieto - squamous 
























breadth, .... 


131p. 


127s. 


129s. 


142s. 


130s. 


123p. 


125p. 


134s. 


121 


128 


130s. 


Cephalic Index, 


78-2 


77-4 


71-3 


85-5 


72-2 


69-1 


68-3 


72-8 


72- 


74- 


76-5 


Horizontal circumference, 


500 


465 


498 


495 


494 


491 


502 


508 


474 


481 


473 


Frontal longitudinal arc, . 


120 


120 


128 


121 


122 


130 


126 


125 


114 


125 


126 


Parietal „ „ . . 


135 


125 


120 


120 


126 


130 


137 


f 253 


120 


118 


120 


Occipital „ „ . . 


115 


96 


110 


103 


113 


96 


107 


105 


105 


106 


Total „ „ . 


370 


341 


358 


344 


361 


356 


370 


378 


339 


348 


352 


Vertical transverse arc, 


310 


283 


290 


305 


296 


285 


292 


292 


269 


281 


288 


Length of foramen magnum, . 


33 


30 


35 


37 


35 


36 


41 


36 


27 


34 


34 


Basi-nasal length, 


106 


93 


100 


98 


102 


91 


96 


102 


91 


100 


96 


Basi-alveolar length, 


103? 


86 


96 


93 


99 


90 


87 


97 


95 


95 


89 


Gnathic Index, 


97-2 


92-5 


96- 


94-9 


97-1 


98-9 


90-6 


95-1 


104-4 


95- 


92-7 


Interzygomatic breadth, . 


126 


121 


119 


131 


131 


122 


124 


134 


119 


123 


123 


Intermalar, . . . . 


116 


107 


109 


120 


118 


112 


111 


120 


114 


112 


112 


Nasio-mental length, 






100 


105 


104 




106 






... 


106 


Nasio - mental complete facial 






















60 


Index, .... 






84' 


80- 










• • • 






Nasio-alveolar length, 




60 


60 


63 


64 


65 


63 


6*7 


58 


59 




Maxillary upper facial Index, . 






50-4 


48- 


79-4 




85- 








86-1 


Nasal height, .... 


47 


44 


48 


49 


50 


46 


47 


47 


42 


45 


46 


Nasal width, .... 


25 


24 


27 


26 


21 


23 


25 


25 


24 


24 


22 


Nasal Index, .... 


53-2 


5J/.-5 


56-8 


58-1 


42- 


50- 


53-2 


53-2 


57-1 


53-3 


47-8 


Orbital width, 


39 


38 


38 


38 


36 


39 


39 


39 


36 


36 


37 


Orbital height, 


35 


31 


29 


35 


32 


36 


34 


31 


31 


30 


32 


Orbital Index, 


89-7 


81-6 


76-3 


92-1 


88-9 


92-3 


87-2 


79-5 


86-1 


83-8 


86-5 


Palato-maxillary length, . 






47 


52 


50 


53 


54 


52 


53 


54 


52 


49 


Palato-maxillary breadth, . 






55 


59 


61 


60 


61 


63 


65 


65 


64 


58 


Palato-maxillary Index, . 






117- 


113-4 


122- 


113-2 


112-9 


121-1 


122-6 


120- 


123- 


118-3 




Symphysial height, . 








28 


27 


22 




30 








28 


03 


Coronoid ,, 








57 


60 


65 




61 








51 




Condyloid „ 








58 


63 


60 




56 








48 




Gonio-symphysial length, . 








83 


82 


80 




89 








81 


o 


Inter-gonial width, . 
Breadth of ascending ramus, 








95 

27 


88 

28 


94 
33 


... 


101 
30 




... 


... 


92 
34 



88 PROFESSOR SIR W. TURNER ON 



Bhima. Table V. 

Two skulls, Nos. 599, 602, presented to the Indian Museum by Mr W. H. P. 
Driver, are marked Bhima race. The former is apparently that of a woman, and the 
latter that of a man who died in Ranchi. I have had a difficulty in determining the 
tribe, caste, or race known as Bhima. I find, however, that Mr Robertson, in his 
Report, p. 183, speaks of Bhimas as vagrants who form a small sub-division of the 
Gonds ; but it is possible that it may be a mis-spelling of Bhaina, a tribe living along 
the southern border of Chuta Nagpur. 

The general form of the skulls in the norma verticalis was an elongated oval 
with the sides of the cranium steep, the parietal eminences not very bulging. The 
sagittal region was not ridged, and the slope downwards to the parietal eminences was 
not very steep. The slope from the obelion to the occipital point was gradual ; the 
occipital squama moderately projected. In both, the length-breadth index was doli- 
chocephalic ; in the male the parietal longitudinal arc exceeded the frontal ; in the 
female they were equal. In each skull the basi-bregmatic diameter was greater than 
the parieto-squamous, and the vertical index was higher than the cephalic. The fore- 
head did not much recede, and the glabella and supra-orbital ridges showed no special 
projection. The nasal bones had not much prominence, and the bridge was concave in 
the vertical direction ; the nasal spine of the superior maxillse was relatively small. In 
the male the anterior nares were narrow, and the index was leptorhine ; in the woman 
it was mesorhine. In the man the upper jaw was orthognathous, in the woman 
mesognathous. In the man the orbital index was mesoseme, in the woman megaseme. 
In both the palato-maxillary index was mesuranic. The cubic capacity was micro- 
cephalic, 1270 and 1170 c.c. respectively. 

Koydwar. Table V. 

The Indian Museum contains the skull, No. 284, of a man named Nagooloo, 50 
years old, from Bijji, Bastar State, Central Provinces. He is said to have been of short 
stature ; skin black ; hair black and soft ; eyes dirty brown ; a moustache ; food rice, 
flesh, fish, vegetables. He is stated in the list sent to me to be of the Koydwar race. 
It is possible that this term may be a mis-spelling for Kotwari, a term applied to the 
caste which performs the service of village watchman. 

The skull was elongated and ovoid in the norma verticalis ; the sides were 
moderately steep, the sagittal region was not ridged, the parietal eminences were much 
in advance of the occipital point, and the occipital squama was rounded and prominent. 
The length-breadth index was 71*3, and the skull was dolichocephalic. The frontal 
longitudinal arc was the longest. The basi-bregmatic height was a little below the 
greatest breadth, and the vertical index, 69 "6, was tapeinocephalic. The anterior nares 
were wide, and the nasal index, 56*3, was distinctly platyrhine. The upper jaw was 



CRANIOLOGY OF PEOPLE OF INDIA. 89 

orthognathic, the gnathic index being only 96. The orbits were low, and the index 
was 76 "3. The palato-alveolar arch was mesuranic. The complete facial index, 84, 
was chamseprosopic. The teeth were much worn. The sutures of the cranial vault 
were nearly obliterated. The skull was cryptozygous. The cranial capacity was 
1267 c.c. 

Bunjana. Table V. 

A skull in the Indian Museum, No. 285, from the Central Provinces from 
Koromankiai near Bastar, marked Bunjana, is probably that of a Banjara or Bunjara. 
It is that of a man set. 40, 5 feet 3 inches high ; he had skin dark brown ; hair 
grey ; eyes dirty brown ; a moustache ; food, rice, mutton, vegetables. The Bunjaras 
are a nomadic class, engaged in the occupation of carrying goods by pack-bullocks. 

This skull did not possess an elongated oval form. When seen from the norma 
verticalis it was more rounded, and its greatest length was only 166 mm. The parieto- 
occipital region was flattened, and as it was not symmetrical, it is probable that arti- 
ficial pressure had been applied during infancy. The length -breadth index was 85*5 
and the skull was hyper-brachycephalic. The frontal longitudinal arc was 1 mm. longer 
than the parietal. The basi-bregmatic height was much less than the greatest breadth, 
and the vertical index was 78 '9. The anterior nares were wide, and the index was 
platyrhine. The upper jaw was orthognathous. The height and width of the orbits 
were almost equal, and the index was megaseme. The palato-maxillary index was 
brachyuranic, and the palate had a wide horse-shoe shape. The face was chamse- 
prosopic, and the complete facial index was only 80. The teeth were much worn and 
stained with betel. The cranial sutures were distinct ; small Wormian bones were 
present in the lambdoidal suture ; the pterion was normal. The skull was cryptozygous. 
The cranial capacity was 1292 c.c. 

Kdmdr and Lohdr. Table V. 

These names are applied to castes who manufacture articles in metal. The 
Kamars work in metals generally ; the Lohars are the blacksmiths or workers in iron. 
The Kamars are found in Bengal and Behar ; * the Lohars in Western Bengal, Behar, 
and Chuta Nagpur. Mr Risley considers that these caste names express only a simi- 
larity in occupations, and do not indicate uniformity in race. He also states that the 
lohar or blacksmith is a recognised official in a Kol village community. Each caste is 
probably composed of persons belonging to different tribes, some of which are probably 
indigenous to the locality, whilst others have migrated into the district in which they 
live, so that they may include Aryans, Aborigines, and crosses between Aryan and non- 

* Mr Robertson, in his Report on the Census in the Central Provinces, p. 190, states that in Raipur a trihe of 
people named Kamar live in remote jungles on fruits and small game, and although in some provinces, as Bengal, 
the term is an occupational one, it includes both aborigines and non-aboriginal people. 



90 PROFESSOR SIR W. TURNER ON 

Aryan people. He supports this view by citing the prevalence of different social 
customs as well as religious differences. Some are orthodox Hindus, others worship 
gods not included in the Hindu mythology. As regards marriage, both infant and adult 
marriage prevail ; widow marriage is allowed by some, but forbidden by others. Some 
groups permit marriage within the group, whilst others are exogamous. Cremation is 
practised by the Kamars. 

I have examined the skull of a Kamar named Bhudny, from Hazaribagh, said to 
be a woman, presented to me by Dr J. J. Hedley Wood ; also that of a Lohar, who 
died at Ranchi, No. 600 in the India Museum. 

The Kamar skull, ovoid in its general form, was long in relation to the breadth ; 
its sides were vertical, but it was not so roof-shaped as in some of the dolichocephali ; 
the length-breadth index was 74, and the frontal longitudinal arc was the longest. 
The basi-bregmatic corresponded with the greatest parieto-squamous diameter. The 
projection of the glabella and supra-orbital ridges gave one the impression of a male 
rather than a female cranium, but the forehead receded very slightly, and the vertex 
was inclined to be flattened ; the parieto-occipital region sloped gently into a rounded 
occipital squama. The nasion was a little depressed ; the bridge of the nose was con- 
cave, but projected at the tip ; the nasal spine of the superior maxillae was moderate, 
and a low ridge separated the floor of the nose from the incisive region. The anterior 
nares were large and platyrhine, the upper jaw was orthognathous ; the orbits were 
mesoseme, and the palate was brachyuranic. There was no lower jaw. The teeth were 
only slightly worn, though some were carious ; the canine and incisive fossae were deep. 
The sutures were unossified ; from their condition and that of the teeth the age was 
probably about 30. There were no Wormian bones, but a large epipteric was in each 
pterion ; with this exception no osseous irregularities were observed. The cranial 
capacity was 1230 c.c. 

The Lohar skull was probably that of a female. Its breadth bore to the length a 
proportion which placed the cranium in the lower term, 76 '5, of the mesaticephalic group, 
and the greatest breadth was about the squamous suture ; the frontal longitudinal arc 
was the longest. The height was somewhat greater than the breadth, and the vertical 
index was 77 '1. The left parieto-occipital region was a little flattened. The nasal bones 
had but little projection,, and the bridge was concave vertically ; the nasal spine of 
the superior maxillae was small. The nose was relatively narrow and with a leptorhine 
index ; the upper jaw was orthognathous, the orbit was mesoseme, and the palate was 
brachyuranic. The face was chamaeprosopic. The cranial capacity, 1240 c.c, was 
microcephalic. 

Ahir-Godld. Table V. 

The Goalds or Gopas are the pastoral caste of India, extensively diffused in the 
North- West Provinces, the valley of the Ganges, Behar, Orissa, and Chuta N&gpur. 
The name Ahir is applied to the whole caste in North-Western India ; but in the south 



CRANIOLOGY OF PEOPLE OF INDIA. 91 

and east it is apparently restricted to one of its divisions, the entire caste being named 
Goala. The Ahir or Goala, whose duty it is to look after the cattle, is, according to Mr 
Kisley, one of the recognised officials of a Kol village community. Colonel Dalton 
groups the Ahirs as Aryans, but in the mountainous districts of Orissa and Chuta 
Nagpur, they seem to have had incorporated with them a proportion of the abori- 
ginal inhabitants, who have become Hinduised. In consequence of this intermixture, 
the physical characters of the caste vary in different localities. Dalton states that the 
Mathurabasis have high, sharp and delicate features, and light brown skins quite of the 
Aryan type ; whilst the Magadhas have coarse features, the skin is dark in colour, the 
hands and feet are large, and the difference between them and the Kol-speaking people 
of Singbhiim is not distinguishable. The intermixture also affects the customs of the 
caste. Marriage usually takes place in infancy, though in Chiita Nagpur adult marriage 
is permitted, and in the hill districts the marriage of widows is sanctioned. Kisley 
states that in Chuta Nagpur a man may not marry a woman of his own totem. Cre- 
mation is practised on the dead bodies of married persons, but not on those of children. 
In religion they are Hindus, and observe the usual festivals. The Ahirs and Goalas 
together numbered, in 1891, about eleven and a half millions of people. 

In the Indian Museum is a skull, No. 27, marked Ahir, Goala caste, which was 
presented in 1863 by Lieut. -Col. Dalton; the man, Teetoo, from Puttea, was hanged 
in Ranchi jail. He is said to have been 25 years old, 5 feet 2 inches high ; hair black, 
long, coarse ; eyes black, set straight in the face ; food, rice, vegetables, and flesh. 

The cranium, seen in the norma verticalis, was a very elongated ovoid, the sides 
vertical, with a slight sagittal ridge, and a slope outwards to the parietal eminences. 
The length-breadth index was 68*3, and the skull was hyper-dolichocephalic ; the parietal 
longitudinal arc was much longer than either the frontal or occipital ; the basi-bregmatic 
height exceeded considerably the breadth, and the vertical index was 7 3 '8. The 
glabella and supra-orbital ridges were moderate ; the forehead was somewhat retreating ; 
the parietooccipital region sloped gently backwards, and was flattened from side to side ; 
the occipital squama was not prominent, and projected very little behind the inion. The 
nasion was slightly depressed ; the bridge of the nose was not prominent, and was con- 
cave from above downwards. The nasal spine of the superior maxillae was distinct, and 
a sharp ridge separated the floor of the nose from the incisive region. The nasal 
index was 53*2, i.e., platyrhine ; the gnathic index, 90'6, markedly orthognathous ; the 
orbital index, 87*2, was mesoseme ; the palato-maxillary index, 121*1, was brachyuranic ; 
the complete facial index was 85, so that the face was chamaeprosopic. The teeth were 
all erupted and a little worn ; the incisive fossae in the upper jaw were deep, and the 
canine fossae were well marked. The cranial sutures were simple, and showed signs of 
commencing ossification. No Wormian bones were present, but a large epipteric bone 
was seen in each pterion. The jugal processes were tuberculated. The lower jaw was 
well developed. The skull was phsenozygous and rested behind on the mastoid-temporals. 
The cubic capacity of the cranium, 1328 c.c, placed it in the microcephalic group. 

VOL. XL. PAET I. (NO. 6). 



92 PROFESSOR SIR W. TURNER ON 



Teli. Table V. 

The Teli or Til i is a banking, trading, and oil-pressing caste in Bengal, Behar, and 
Orissa. Some are Hindus, others Mahommedans in religion. In Bengal, amongst the 
richer classes, they permit infant marriage and forbid the marriages of widows. In 
Orissa, again, they adhere more to aboriginal customs ; they hold, says Mr Eisley, 
totems in reverence. Infant marriage is not essential, and widow marriage is allowed. 
They cremate the dead. They number from 4,000,000 to 5,000,000 of people. 

Two crania of this caste have come under my observation ; one, No. 598 in the 
Indian Museum, a male from the village Pittoria, near Ranchi, Chiita Nagpiir ; the 
other a female, presented to me by Dr Hedley Wood, from Raipur in the Central 
Provinces. The general form in the norma verticalis was the elongated ovoid so 
frequently referred to in the preceding descriptions of the dolichocephalic crania of the 
aborigines ; this form being associated with vertical sides and a rounded occipital 
squama. The length-breadth index in the man was 72*8, and the basi-bregmatic 
diameter exceeded the parieto-squamous ; in the woman the index was 72 ; the basi- 
bregmatic height was much below the parieto-squamous diameter, and the parietal 
longitudinal arc was longer than the frontal. The forehead was not receding ; the 
glabella and supra-orbital ridges were not prominent. The nasal bones were not 
projecting, and the bridge was flattened ; the nasal spine of the superior maxillae was 
moderate ; a ridge marked off the floor of the nose from the incisive region of the 
upper jaw ; the anterior nares were wide, and the index in each specimen was platy- 
rhine. In the Teli man, the upper jaw w 7 as orthognathous, in the woman prognathous. 
In the man the orbital index w T as microseme, in the woman mesoseme. In both, the 
palato-maxillary index was just within the brachyuranic group. In the woman's skull 
there were no osseous irregularities. The cranial capacity in the man was 1370 c.c. ; 
in the woman it was only 1005 c.c. 

Uriya. 

In addition to the crania described in the preceding part of this memoir, which are 
definitely associated with particular races, tribes, or castes, the Indian Museum contains 
a number of skulls from Orissa, marked in the catalogue Ooria or Uriya. Uriya is a 
linguistic term, which expresses a particular derivative of Sanskrit. It is the mother 
tongue of a very large percentage, said to be 95*1 per cent., of the Hindu population 
of Orissa, of those who inhabit the plains as distinguished from the aborigines who live 
in the mountains, and the name of the language is given to the people who speak 
it. As the aborigines of this province speak either Dravidian or Kolarian, the Uriya 
tongue of the Hindu population in Orissa contains a mixture of archaic forms and words 
derived from those languages. Uriya-speaking people form a considerable proportion 
of the class of domestic servants in the north-east of India, which probably accounts for 



CRANIOLOGY OF PEOPLE OF INDIA. 93 

the number of crania in the Indian Museum marked Uriya, most of which had been 
obtained from the medical school of Calcutta. 

I have examined thirty skulls from the Indian Museum, marked Uriya in the list 
sent to me, and in addition I have received from my friend Major Bannerman, M.D., 
two specimens which he had collected at Baghmari village in Orissa. 

The crania were by no means a homogeneous series, but varied materially in form 
and proportions, so that it would be impossible to draw up a description which would 
be generally applicable. If we take the proportion of length and breadth to guide us 
in our examination, we shall find that the crania can readily be arranged in three 
groups. The larger number, seventeen in all, have the length-breadth index below 75, 
and in form and proportions are dolichocephalic ; in ten skulls the corresponding index 
is between 75 and 80, mesaticephalic ; whilst in five crania this index was upwards of 
80, brachycephalic. 

Dolichocephalic Series.- — Of the seventeen crania belonging to this group, fifteen 
were apparently males and two females. They were all adults, with perhaps two ex- 
ceptions about 20 and 21 years of age. When examined in the norma verticalis, they 
were seen to be elongated and ovoid in outline, with side walls approaching the vertical 
and with no great difference between the frontal and parietal transverse diameters. 
The parietal eminences were fairly marked. As a rule, the sagittal line was not raised 
above the general plane of the vertex, and the slope from it to the parietal eminence 
was moderate. In the majority the parieto-occipital region sloped gently backwards 
and downwards, but in four specimens it was inclined more abruptly, and in three of 
these it showed a want of symmetry, as if modified by artificial pressure. In No. 232 
this character was most distinct, and in it was also seen a transverse post-coronal 
depression, as if from wearing a tight band during infancy. In No. 42, the elongated 
form was exaggerated and the skull was hyper-dolichocephalic ; the sagittal suture was 
unossified, but the right parieto-mastoid and adjoining parieto-squamous were closed. 
The mean cephalic index of the series was 72*2. The male skulls in the greatest length 
ranged from 171 to 194 mm., but the majority were between 180 and 187 mm. In the 
greatest breadth they ranged from 124 to 139 mm., but the majority were between 127 
and 134 mm. In no specimen was the occipital arc the longest ; in several, the frontal 
and parietal longitudinal arcs were equal or almost equal ; in a few, the frontal 
materially exceeded the parietal, in others the proportion was reversed. The mean 
vertical index of the series was 75*4, and in only three crania was the basibregmatic 
height less than the greatest breadth. (Table VI.) 

The glabella and supra-orbital ridges had, as a rule, but little prominence, though 
well marked in the man from Baghmari village. In the men the forehead was slightly 
receding, but in the women it was almost vertical. The nasion was only slightly de- 
pressed ; as a rule, the bridge of the nose projected forwards, but in a few it was not 
prominent. The nasal spine of the superior maxillse was distinct as a rule, and the 
floor of the nose was separated from the incisive region of the maxilla by a sharp ridge. 



94 PROFESSOR SIR W. TURNER ON 

The nasal index in sixteen skulls ranged from 45*8 to 56, and the mean was 51 "6, i.e., 
mesorhine, to which group eight specimens belonged ; of the remainder, two were 
lcptorhine, and six were platyrhine. The projection of the upper jaw was ortho- 
gnathous, the mean gnathic index of fifteen crania being 96*2 ; no specimen was 
prognathous, and only four were mesognathous. The orbits were measured in sixteen 
crania, and the mean index was 85*6, mesoseme, to which group eight specimens 
belonged ; five specimens were microseme and only three were megaseme. The palato- 
maxillary index showed a great range of variation, and indicated marked differences in 
the relative length and breadth of the palate and alveolar arch ; five specimens were 
dolichuranic, six were mesuranic, six were brachyuranic ; in several specimens the 
palate had a high arch. The nasio-mental diameter was taken in only seven skulls, in 
five of which the proportion between that diameter and the interzygomatic breadth was 
chamasprosopic, in the remaining two, leptoprosopic. 

The cranial sutures were simple and, as a rule, not ossified. In ten skulls the 
lambdoidal suture contained Wormian bones, and in one of these they were numerous. 
In seven crania an epipteric bone or bones was present either on one or both sides, but 
in none did the squamous-temporal and frontal directly articulate. No skull was 
metopic. In No. 414 the basi-cranial synchondrosis was not ossified, and the upper 
wisdom teeth were not erupted ; in the right orbit a slender process of the orbital plate 
of the superior maxilla ascended between the os planum and the lachrymal to articulate 
with the frontal. I have previously recorded examples of this variation in human crania 
in Bush, Papuan, and Lushai skulls.* Several specimens retained the infra-orbital 
suture. The muscular ridges and processes were not strongly marked. The skulls were 
cryptozygous. No specimen showed a paramastoid process, third condyl or auditory 
exostosis. In three crania the wisdom teeth had not appeared. The mean cranial 
capacity of fifteen male skulls was 1370 c.c, mesocephalic ; and the range was from 
1138 c.c. to 1660 c.c. The mean capacity of two female skulls was 1370 c.c. 

Mesaticephalic Series. — Of the ten crania which belonged to this series, seven were 
apparently males and three females. They were all adult except No. 20, in which, 
though the wisdom teeth were erupted, the basi-cranial synchondrosis was not ossified. 

Of these specimens, seven had a cephalic index between 75 and 77 '5, whilst three 
ranged from 77'6 to 79'6. Those with the lower indices showed no great difference in 
the general form of the cranium from the dolichocephalic group, whilst those in the 
higher series approximated to the brachycephalic, to be next described. (Table VII.) 

Two skulls were so steep and vertical in the parieto-occipital region as to give the 
impression that they had been artificially flattened. In four skulls the basi-bregmatic 
height was less than the greatest breadth ; in three it was greater ; in three they were 
equal. In all, the occipital longitudinal arc was less than either the parietal or frontal ; 
in four the frontal exceeded the parietal ; in four the opposite condition existed. 

The glabella and supra-orbital ridges were moderate, but in No. 130 they were 

* Trans. Roy. Hoc, Edinburgh, 1899, vol. xxxix. p. 712. 






CRANTOLOGY OF PEOPLE OF INDIA. 



Table VI. 



95 



Uriyd. — Dolichocephali. 









J3 






A 
















°' -; 


._• 




._: 


paul. 
ttack, 
issa. 


Xi 


+s 






-4J 
















-4-> O 


ca 




3 




3 CO 


3 . 
3 co 


■%% 




3 
3 .>> 




§ i 

§..2 


*72 W 


-c3 * 


-C3 « 
.&. a 




« r |~>> 


zeun 
lasoi 
issa. 


3 c8 




so.SS 




O 3 - 




— °C 






^a Q 


c5 C 






J- '^ 






rt «S "jh 


o c8 i. 


c3 i- 




a s~> 




ooo 


Wo 


wo 


HP 


3kj3 


mt> 


Ph£> 


35 


GO 


PO 


55 


P 


£Kt> 


MWO 


MO 


DO 


P30 




I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


E. IT. A.M. 


I.M. 


E.U.A.M. 


C lection number, 


2 


149 


54 


20 


23 


32 


33 


179 


232 


409 


412 


419 


24 


42 




414 






28 


23 


45 


27 


23 


38 


24 


30 


18 


Ad. 


Ad. 


Ad. 


65 


20 


Ad. 


Ab. 21 


Ad. 




M 


M 


M 


M 


M 


M 


M 


M 


M 


M 


M 


M 


M 


M 


M. 


F. 


F. 


Cbic capacity, 


1345 


1455 


1308 


1448 


1350 


1305 


1232 


1300 


1348 


1660 


1485 


1138 


1334 


1406 


1440 


1396 


1130 


Cibello-occipital length, 
Isi-bregmatio height, . 


181 


180 


174 


187 


177 


180 


176 


175 


177 


194 


180 


171 


182 


186 


184 


182 


168 


143 


146 


130 


140 


130 


126 


137 


138 


134 


138 


146 


129 


135 


136 


135 


138 


122 


1 firtical Index, . 


79-0 


81-1 


74-7 


74-9 


73-4 


70 -0 


77-8 


78-9 


75-7 


71-1 


81 -1 


75-4 


74-2 


73-1 


73-4 


75-8 


72'6 


Suimum frontal dia- 




































neter, .... 


92 


95 


90 


95 


91 


89 


99 


96 


92 


97 


91 


95 


101 


91 


99 


92 


92 


Esphanic 


106 


114 


112 


109 


109 


113 


114 


109 


108 


113 


112 


107 


113 


106 


105 


109 


102 


^terionic, 


100 


100 


100 


109 


109 


99 


97 


103 


104 


108 


108 


98 


100 


98 


106 


96 


95 


(eatest parieto-squamous 




































Dread th, 


127p. 


133s. 


127s. 


134s. 


129p. 


133p. 


127s. 


130p. 


128p. 


139s. 


132p. 


127s. 


129s. 


124p. 


134s. 


128p. 


125p. 


(fihalic Index, . 


70 -2 


■73 -9 


73-0 


71-7 


72-9 


73-9 


72-2 


74S 


72S 


71-6 


73-3 


74S 


70-9 


66-7 


72-8 


70S 


74-4 


Lrizontal circumference. 


495 


501 


486 


516 


488 


499 


491 


488 


488 


538 


507 


485 


505 


502 


510 


500 


464 


lontal longitudinal arc, 


130 


130 


130 


137 


129 


134 


137 


124 


130 


130 


147 


128 


128 


138 


137 


135 


128 


Irietal ,, ,, 


130 ) 


248 


130 


139 


128 


125 


124 


130 


138 


130 


124 


126 


131 


142 


134 


134 


116 


( cipital , , , , 


110 \ 


99 


116 


113 


114 


107 


105 


99 


127 


110 


99 


109 


112 


109 


103 


101 


Ital ,, ,, 


370 


378 


359 


392 


370 


373 


368 


359 


367 


387 


381 


353 


368 


392 


380 


372 


345 


i "* rtical transverse arc, . 


310 


314 


298 


309 


302 


303 


308 


300 


302 


320 


322 


288 


302 


302 


306 


309 


279 


Ingth of foramen mag- 




































num, .... 


35 


35 


32 


33 


34 


32 


33 


34 


31 


36 


34 


29 


33 


35 


36 


35 


31 


llsi-nasal length, . 


106 


104 


102 


101 


94 


95 


102 


102 


101 


111 


107 


98 


102 


99 


101 


102 


93 


lisi-alveolar length, 


95 


96 


100 


98 


94 


94 


98 


97 


96 


111 


100 


95 




96 


98 


97 


93 


t\,athic Index, 


89-6 


92S 




97 


100 


98-9 


96-1 


95 -1 


95- 


wo- 


93-5 


96-9 




97- 


97- 


95 -1 


100- 


]|terzygomatic breadth, . 


126 


133 


124 


127 


114 123 


126 


128 


130 


rn 


125 


123 


125 


123 


131 


118 


122 


]|termalar , , 


114 


116 


112 


116 


103 


111 


116 


120 


118 


121 


112 


113 


115 


111 


120 


107 


113 


ijisio-mental length, 


124 


119 












114 


105 










108 


122 




104 


jisio-alveolar, . 


73 


66 


62 


66 


62 


64 


65 


66 


60 


72 


67 


62 




64 


69 


59 


56 


implete Fecial Index, . 


98-4 


89-4 












89- 


80- 










87-8 


93-1 




83-6 


hsal height, 


51 


46 


46 


46 


47 


49 


48 


48 


47 


51 


51 


46 


53 


45 


50 


46 


43 


lisal width, 


24 


25 


26 


25 


23 


24 


25 


22 


23 


28 


26 


24 


27 


23 


28 


25 


24 


.anal Index, 


47-1 


54S 




54-3 


48-9 


49 


52-1 


45-8 


48-9 


54-8 


51- 


52-2 


50-9 


51-1 


56- 


54-3 


55-8 


('bital width, . 


37 


36 


35 


38 


36 


38 


38 


37 


37 


40 


39 


39 


39 


38 


40 


37 


35 


i-bital height, 


36 


33 


29 


32 


31 


31 


29 


32 


32 


33 


32 


32 


35 


33 


34 


32 


30 


i -bital Index, 


97-3 


91-7 




84-2 


86-1 


81-6 


76-3 


86-5 


86-5 


82-5 


82- 


82- 


89 7 


6-8 


85- 


86-5 


S5-7 


Mato-maxillary length, 


53 


54 


55 


57 


54 


53 


55 


56 


52 


63 


54 


55 


51 


3 


52 


52 


50 


"dato-maxillary breadth, 


65 


65 


62 


59 


58 


57 


63 


63 


58 


71 


57 


68 


60 


56 


70 


63 


60 


th tin -maxillary Index, 


120-7 


120S 


112-7 


103-5 


107-4 


107-5 


114-5 


112-5 


111-5 


112-7 


105-5 


123-6 


117-6 


105-6 


134-6 


12V 


120- 


{ Symphysial height, 


33 


35 




33 


28 


28 


27 


30 


29 


36 


31 


29 


27 


30 


37 


25 


30 


j Coronoid ,, 


69 


60 




70 


56 


67 


54 


59 


57 


62 


58 


61 


66 


67 


60 


64 


69 


Condyloid ,, 


63 


60 




67 


57 


60 


54 


63 


52 


65 


64 


57 


59 




59 


59 


69 


. J Gonio - symphysial 

length, . 




































92 


85 




89 


79 


90 


87 


92 


84 


87 


92 


82 


82 


87 


86 


84 


87 


Inter-gonial width, 




































, ] outside, . 


105 


100 












98 


92 










96 


98 




93 


j Breadth of ascend- 




































1 ing ramus, 


33 


32 




38 


29 


40 


33 


35 


29 


34 


29 


34 


29 


34 


35 


33 


33 







































96 PROFESSOR SIR W. TURNER ON 

strongly marked. The forehead only slightly receded. The nasal bones were 
prominent and with usually a good bridge, but in No. 65 the bridge was flattened. 
The nasal spine of the superior maxillse was moderate ; in some specimens the nasal 
floor was separated from the incisive region by a ridge ; in others, as in No. 65, they 
rounded off into each other. In seven specimens the nasal index was mesorhine ; in 
one, leptorhine ; in two, platyrhine. In six crania the upper jaw was orthognathous ; 
in two, mesognathous, and in one, No. 65, prognathous. In six the orbital index was 
mesoseme ; in three, microseme ; in one, megaseme. As regards the relative length and 
breadth of the palato-alveolar arch, five specimens were mesuranic, one was dolichuranic, 
two were brachyuranic. The four crania in which the length of the entire face could 
be taken, were practically leptoprosopic or high faced. 

The cranial sutures, as a rule, were simple ; in four skulls, Wormian bones were 
present in the lambdoidal suture, and in one of these, No. 65, the right half of the 
upper occipital was an independent bone; in No. 415, two sutnral bones were in the 
sagittal behind the obelion. In one skull on both sides, and in another on the left side, 
the squamous temporal articulated with the frontal ; in three crania, epipteric bones 
were present, in two of these on both sides, in one on one side. Three skulls showed 
the infra-orbital suture. One skull, No. 98, was edentulous ; in one, the teeth were 
stained with betel. No skull was metopic, or possessed a third condyl, paramastoid 
process or auditory exostosis. They were cryptozygous, and mostly rested behind on 
the occipital bone. The muscular ridges and processes were not strong. The mean 
cranial capacity in the men was 1336 c.c, and ranged from 1212 to 1530 c.c. ; in the 
three women, the mean capacity was 1176 c.c. 

Br achy cephalic Series. — Five of the crania marked Uriya were brachy cephalic 
in form and proportions. Three were apparently males and two females. (Table VIII.) 
In the norma verticalis the crania were rounded, and the male skulls, with one 
exception, had a less glabello-occipital length than the shortest male skull in the 
dolichocephalic group ; whilst the female skulls were shorter than the female dolicho- 
cephalic Uriyas. The sagittal region was not ridged, and the crania generally were 
more flattened at the vertex than in the dolichocephali. The parietal eminences were 
prominent, especially in No. 38, and in the norma occipitalis the skulls had a 
pentagonal form. In four crania there was evidence of parietooccipital flattening, 
more particularly in the h}^per-brachycephalic skull, No. 417, in which the parieto- 
occipital region was almost vertical ; the pressure had produced in two skulls an 
unsymmetrical projection to the right, and in two others to the left. In No. 38 the 
occipital region was rounded, and projected behind the inion. The cephalic index 
ranged from 80 to 88*2, and the mean was 83*7. In all, the occipital longitudinal arc 
was the shortest ; in three, the frontal arc was longer than the parietal ; in two, the 
parietal was the longer. In all, the basi-bregmatic diameter was less than the parieto- 
squamous, and the mean vertical index was 79*2. 

The glabella and supra-orbital ridges were feeble ; the forehead was almost vertical ; 



CRANIOLOGY OF PEOPLE OF INDIA. 



97 



Table VII. 

Urtyd. — Mesaticephali. 





Matu. 
Hindu. 


Bho- 
blanee. 


Gaily. 


Bassu. 


Orissa. 


Orissa. 


Orissa. 


Orissa. 


Oiissa. 


Orissa. 






Oiissa. 


Hindu. 
Orissa. 


Orissa. 


Oiissa. 


















I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


Collection number, 


65 


76 


98 


130 


199 


413 


415 


410 


416 


418 




Age, 


20 


30 


70 


50 


38 


Ad. 


Ad. 


Ad. 


Ad. 


Ad. 




Sex 


M. 


M. 


M. 


M. 


M. 


M. 


M. 


F. 


F. 


F. (?) 




Cubic capacity, . 


1260 


1212 


1205 


1530 


1408 


1336 


1405 


1270 


1110 


1150 




Glabello-occipital length, 


174 


169 


167 


185 


175 


173 


179 


170 


168 


168 




Basi-bregmatic height, . 


132 


128 


130 


150 


132 


134 


128 


136 


128 


132 




Vertical Index, 


75-9 


75-7 


77'8 


81'1 


75'4 


77-5 


71-5 


80- 


76-2 


78-6 




Minimum frontal diameter, . 


94 


95 


88 


100 


98 


94 


90 


91 


91 


88 




Stephanie, .... 


114 


115 


104 


120 


115 


108 


111 


109 


108 


103 




Asterionic, .... 


103 


95 


102 


115 


98 


104 


105 


101 


90 


102 




Greatest parieto-squamous 
























breadth, .... 


137p. 


128p. 


133p. 


141s. 


135p. 


134s. 


135p. 


132p. 


128p. 


128p. 




Cephalic Index, . 


78-7 


75-7 


79-6 


76'2 


77-1 


77-5 


75-5 


77-6 


76-2 


76-2 




Horizontal circumference, 


494 


480 


475 


518 


493 


495 


500 


480 


472 


470 




Frontal longitudinal arc, 


120 


122 


130 


138 


131 


124 


130 


124 


124 


119 




Parietal ,, ,, ) 


243 


236 | 


115 


125 


134 


118 


134 


131 


118 


120 




Occipital „ „ J* 


111 


114 


100 


112 


112 


107 


99 


109 




Total 


363 


358 


356 


377 


365 


354 


376 


362 


341 


348 




Vertical transverse arc, 


312 


285 


309 


319 


315 


298 


308 


303 


293 


295 




Length of foramen magnum, 


29 


31 


31 


33 


37 


33 


34 


35 


31 


30 




Basi-nasal length, 


97 


96 


93 


106 


97 


99 


93 


98 


100 


99 




Basi-alveolar length, 


100 


97 


■ • • 


95 


96 


95 


88 


94 


91 


95 




Gnathic Index, 


1031 


101' 




89-6 


99- 


96' 


94-6 


95-9 


91- 


96- 




Interzygomatic breadth, 


124 


117 


118 


133 


126 


124 


123 


117 


116 


118 




Intermalar „ 


116 


110 


106 


120 


117 


116 


116 


107 


104 


110 




Nasio-mental length, . 


109 


116 




120 


120 


... 




■ • • 


• • • 






Nasio-alveolar ,, 


61 


68 


... 


69 


66 


68 


60 


63 


61 


63 




Complete Facial Index, 


89-5 


99' 


• > • 


90- 


95- 


... 


• * • 




• •• 






Nasal height, 


46 


50 


43 


52 


50 


49 


46 


46 


46 


47 




Nasal width, 


23 


24 


20 


25 


25 


26 


23 


23 


23 


27 




Nasal Index, 


50- 


48- 


46-5 


48-2 


50' 


53-1 


50- 


50' 


50- 


57% 




Orbital width, 


38 


37 


36 


39 


39 


37 


37 


36 


38 


38 




Orbital height, 


31 


30 


32 


35 


35 


33 


34 


30 


34 


32 




Orbital Index, 


81-6 


81 1 


88-9 


89-7 


89-7 


89'2 


91-9 


83'3 


89-5 


84-2 




Palato-m axillary length, 


59 


53 


• • • 


52 


56 


54 


51 


53 


49 


52 




Palato-maxillary breadth, 


63 


61 


• • • 


64 


64 


63 


60 


59 


57 


63 




Palato-maxillary Index, 


106-7 


115' 


• • • 


123- 


114-3 


116-6 


117-6 


111-3 


116-3 


121' 






Symphysial height, 


28 


31 




28 


36 


29 


33 


28 


25 


29 




g: 


Coronoid „ 


56 


63 


57 


61 


63 


62 


60 


59 


58 


61 






Condyloid „ 


58 


66 


58 


66 


63 


59 


56 


48 


52 


54 




53 ■{ Gonio-symphysial length, 


90 


83 


72 


97 


87 


80 


87 


85 


76 


81 






Inter-gonial width, outside, 


92 


91 




105 


90 










• • • 




^ 


Breadth of ascending 


























ramus, 


42 


33 


27 


35 


30 


35 


35 


30 


31 


33 





98 



PROFESSOR SIR W. TURNER ON 



Table VIII. 
Uriyd. — Brachycephali. 







Siplo. 






Puttonez. 






1 




Hindu. 






Hindu. 










Orissa. 


Hindu. 
Oiissa. 


Orissa. 


Oiissa. 


Cuttack, 
Orissa. 










I.M. 


I.M. 


I.M. 


I.M. 


I.M. 


Collection number, ..... 


4 


129 


411 


417 


38 








Age 




20 


32 


Ad. 




40 








Sex, ...... 




M. 


M. 


M. 


F. 


F. 








Cubic capacity, .... 






1148 


1200 


1118 


1240 








Glabello-occipital length, 




173 


161 


163 


152 


167 








Basi-bregmatic height, 




139 


128 


126 


126 


127 








Vertical Index, .... 




80S 


79-5 


77S 


82-9 


76- 








Minimum frontal diameter, 




82 


90 


88 


88 


83 








Stephanie, ..... 




116 


112 


109 


106 


104 








Asterionic, ..... 




106 


97 


99 


93 


97 








Greatest parieto-squamous breadth, . 




140p. 


138 p. 


135p. 


134p. 


135p. 








Cephalic Index, .... 




80-9 


85-7 


82-8 


88-2 


80-8 








Horizontal circumference, 




488 


478 


473 


452 


466 








Frontal longitudinal arc, . 




130 


124 


131 


117 


118 








Parietal „ ,, . . 




128 


117 


120 


119 


125 








Occipital ,, ,, 




105 


100 


99 


92 


112 








Total „ „ . 




363 


341 


350 


328 


355 








Vertical transverse arc, . 




314 


302 


307 


300 


290 








Length of foramen magnum, . 




37 


29 


32 


34 


33 








Basi-uasal length, 




101 


96 


94 


88 


87 








Basi-alveolar length, 




95 


96 


96 


86 


87 








Gnathic Index, 




94-1 


100' 


102-1 


97-7 


100- 








Interzygomatic breadth, 




123 


122 


120 


110 


115 








Intermalar ,, 




109 


112 


109 


100 


102 








Nasio-mental length, 




109 


96 


... 




96 








Nasio-alveolar ,, 




62 


60 


64 


56 


58 








Complete Facial Index, 




88-6 


786 


... 




83-4 








Nasal height, 




48 


48 


45 


43 


43 








Nasal width, 




24 


24 


24 


19 


22 








Nasal Index, 




50- 


50- 


53-3 


M» 


51-2 








Orbital width, 




36 


37 


33 


34 


36 








Orbital height, 




31 


30 


29 


31 


30 








Orbital Index, 




86-1 


81-1 


87-9 


91-2 


83-3 








Palato-maxillary length, 




50 


56 


58 


49 


48 








Palato-maxillary breadth, 




61 


61 


60 


56 


58 








Palato-maxillary Index, 




122- 


109- 


104-4 


114-3 


120-8 








[ Symphysial height, 




28 


25 


33 


30 


24 








| j Coronoid ,, 




53 


60 


58 


53 


60 








'2 I Condyloid 
£ J Gonio-syinphysial length, . 




51 


59 


56 


54 


53 










86 


90 


81 


73 


78 








o 


Inter-gonial width, outside, 




95 


90 


... 


... 


79 








Breadth of ascending ramus, 




35 


35 


34 


28 


28 









CRANIOLOGY OF PEOPLE OF INDIA. 99 

the nasion was not de]3ressed ; the bridge of the nose was not very prominent ; the nasal 
spine of the superior maxillae was moderate ; the floor of the nose in some specimens 
was separated from the incisive region by a sharp ridge. The mean nasal index was 
497, mesorhine, to which group three specimens belonged : one was leptorhine, one 
platyrhine. The mean gnathic index was 9 8 '7, mesognathous, to which group three 
specimens belonged, but two were orthognathous. The mean orbital index was 85 '9, 
mesoseme, to which group two skulls belonged ; one was megaseme ; two were micro- 
seme. The relative length and breadth of the palato-alveolar arch showed great varia- 
tion : two skulls were dolichuranic ; one mesuranic ; two brachyuranic. In all the face 
was chamaeprosopic. 

No skull was metopic. The cranial sutures were simple. In two specimens the 
lambdoidal suture contained Wormian bones ; in one there was a right epipteric bone ; 
in two the infra-orbital suture was present. The crania were cryptozygous. The mean 
cranial capacity of two males was 1174 c.c, and of two females 1179 c.c. ; each skull 
was microcephalic. 

Comparison of Aboriginal Crania. 

Before proceeding to consider the relations, as regards race, which the Dravidian 
and Kolarian-speaking tribes bear to each other, it will be advisable to examine the 
evidence of the possible presence in India of a people more ancient even than the present 
wild tribes of the hill districts. From time to time objects have been found, which, 
from the material of their construction and the simplicity of the workmanship, would 
point to the existence in India of people who manufactured and employed tools and 
implements of stone. 

In 1842 Dr W. H. Primrose found at Lingsoo-goor* ne ar a tumulus on which the 
mess-house of the Hyderabad contingent was built, knives and arrow heads made of 
cornelian, jasper, agate, and chalcedony. 

In 1863 Mr R. Bruce Foote discovered in the Madras Presidency, in situ, in beds 
of a red ferruginous clay mingled with sand and gravel, and at an elevation of 300 feet 
above the sea, chipped implements formed of quartzite.t Stone implements have also 
been obtained by other collectors in Orissa, Mirzapore, Jubbulpoor, and the South 
Mahratta country. Although formed of quartzite and not of flint, Sir John Evans J 
considers that, as far as general form is concerned, they are identical with the imple- 
ments from European river-drifts, and he regards them as belonging to palaeolithic times. 
Mr F. Swynnerton states § that quartzite implements of palaeolithic type have been 
found on the surface of the ground at Raipur. 

Sir John Evans has recorded a worked arrow head from India in the possession of Pro- 
fessor Buckman which belonged to the late Stone age. A number of arrow heads, with 

* Meadows Taylor in Journ. Ethno. Soc, London, N.S., vol. i. p. 175, 1869. 

t Geological Magazine, vol. xi. p. 503. 

I Ancient Stone Implements, 2nd ed., p. 651, London, 1897. 

§ Journ. Anthro. Inst., 1899, vol. ii. p. 141. 

VOL. XL. PART I. (No. 6). P 



100 PROFESSOR SIR W. TURNER ON 

stone beads, a celt, a perforated stone and other objects, formed of chert, chalcedony, 
rock crystal, and quartz have been found by Mr W. H. P. Driver at Eanchi in 
Chiita Nagpiir. They have been described and figured by Professor J. Wood-Mason. * 
The place where they were found had obviously been a neolithic settlement. Mr 
Swynnerton has described roughly chipped fragments of jasper and chert in the 
gravel of the Sourrka river, from the alluvium of the plain in which the city of Gwalior 
is built. 

We can scarcely expect to trace a direct continuity between the present aborigines 
and those prehistoric men who manufactured the primitive palaeolithic implements. It 
is, however, worthy of consideration if some of the existing hill tribes may not be the 
descendants of the people of neolithic times. 

Of the hill tribes referred to in the earlier pages of this memoir the Juangs are 
without doubt the most primitive. Colonel Dalton speaks decidedly on this point, and 
regards them as representatives of the Stone age. Until strangers came amongst them, 
they had no knowledge of metals, they had no word in their language to designate iron 
or other metals, and they employed implements made of stone. They could neither 
spin nor weave, nor had they the simplest knowledge of pottery. They wore no clothes 
but leaves, and were remarkably shy and timid. Although their language is in part 
Kolarian, like that of the Hos and Santals, they have many words which cannot be 
connected with the languages now spoken by other people in India, and the people 
themselves claim to be the autochthones in Keunjhar. 

Like other primitive people they are of low stature ; they have thick lips and, 
according to Dalton, coarse frizzly hair, though the two girls drawn from photographs 
in his great work do not support this statement, as the hair is long and wavy. The 
colour of the skin is not black, but reddish brown. 

In an account which Dr Shortt has given t of the Juangs, Juags, or leaf wearers 
of Orissa, met with by him in the tributary Mahals of Cuttach, he states that the head 
is well formed and globular, the forehead expanded, the cheek bones high, nasal ridge 
depressed and wide, lips fleshy, chin pointed, face triangular or wedge-shaped ; eyes 
large and expressive, a character which scarcely conforms to the Mongolian type of 
countenance which he ascribes to the Juangs. The hair is copious and long on the 
head, moustache and beard scanty. He attaches importance to the large proportion of 
persons in whom the lower jaw is ' underhung.' The average stature of the men is 
5 feet 1^ inches, of the women 5 feet. J 

If the two skulls in the Indian Museum which I have measured are genuine speci- 
mens of the Juang race, it will be seen that whilst the male is dolichocephalic, the index 

* Journal Asiatic Soc. Bengal, vol. lvii. part xi., 1888. 

t Journ. of Anthropo. Soc, p. cxxxvi. in Anthropological Review, vol. iii., 1865. 

X M. J. Walhouse has described, Journ. Anth. Inst, 1875, vol. iv. p. 369, a leaf wearing tribe, named Koragar, 
in South Canara, on the western coast of India. The leaves are worn by the women, a survival, apparently, of a habit 
prior to the use of raiment, but outside the clothes. The people are black skinned, thick lipped, nose broad and flat 
hair rough and bushy. The men, he says, seldom exceed in stature 5 feet 6 inches, but this is probably too high an 
estimate of their stature. 



CRANIOLOGY OF PEOPLE OF INDIA. 101 

of the female is about the middle of the mesaticephalic group ; both were orthognathous 
and platyrhine. The breadth in the malar and zygomatic regions was not so great as to 
give the impression that the face was markedly broad ; but from the absence of the 
lower jaw the proportion between the length and breadth of the entire face could 
not be obtained. The general dimensions of the woman's skull were small, and its 
cranial capacity, 1030, was in the lowest category of human skulls. In the man, 
however, the capacity was higher than is customary in the skulls of savage races. If we 
are to regard these people, and some of the primitive tribes in Southern India described 
by Mr Edgar Thurston, as prse-Dravidian, there is no evidence that they are Negritos. 

It is customary, in speaking of the existing natives of India, to consider that they 
belong to four ethnic types — Mongolian, Kolarian, Dravidian and Aryan or Indo-Aryan. 
The possibility of the presence of a Negrito element should also be made the subject 
of enquiry. 

The Mongolians or Tibeto-Burmans are found on the northern and eastern confines 
of India, and on the east of the Bay of Bengal. I have described representative 
people of this type in Part I. of this Memoir.* 

The Kolarians and Dravidians, on account of linguistic differences, have been by 
many writers regarded as two distinct ethnic types. It has been assumed that the 
Kolarian invaders had preceded the Dravidian, and had migrated into India through 
the north-east passes. The Dravidians, again, are stated to have found their way into 
the Punjab by the north-west passes, and to have spread into Central and Southern 
India, though others have conjectured that they came from the south and east.t They 
are regarded as older inhabitants than the Aryans, who are thought to have entered 
India, something more than 4000 years ago, from the Hindu Kush, the Pamir plateau, 
and the high valley of Cashmere. The aborigines of the hill districts in Southern 
India, the Central Provinces and the Lower Provinces of Bengal, have been described 
as in part Kolarians and in part Dravidians. 

Mr B. H. Hodgson, in his essay on the Kocch, Bodo and Dhimal tribes, | uses the 
term Tamulian as equivalent to aboriginal, and, whilst the people of the sub-Himalayan 
district belong to the Tibetan stock, and those further east to the Chinese, he regards 
those to the south as Tamulian, and as represented by the Kols, Bhils, Gonds, Oraons 
and Mundas. He is of opinion that amongst the Tamulians the physical type is 
essentially the same in all the tribes. 

During the last ten years, and principally through the influence of the writings of 
Mr H. H. Risley,§ the distinction between Kolarian and Dravidian-speaking tribes has 
come to be regarded as only linguistic, and not as representing differences in physical 
type. " The Male of the Rahjmahal hills," he says, " and the Oraons of Chota Nagpore, 
both of whom speak languages classed as Dravidian, are identical in point of physique 

* Trans. Roy. Soc. Edin., vol. xxxix., 1899. 

t Sir W. W. Hunter's Indian Empire and Thurston's Madras Bulletin, 1899, p. 195. 

J Calcutta, 1847. 

§ Tlie Tribes and Castes of Bengal, 1891. 



102 PROFESSOR SIR W. TURNER ON 

with the Miindas and Santals, who are classed on linguistic grounds as Kolarian." 
He does away with the term ' Kolarian ' as having an ethnic significance, and he in- 
cludes both sets of people under the common term ' Dravidian.' Mr Risley's conclusions 
were arrived at after a series of anthropological examinations and measurements, con- 
ducted under his supervision, on about 6000 living persons in Bengal, the North- Western 
Provinces and the Punjab. He defines the Dravidian type as follows : — Head usually 
inclined to be dolichocephalic ; nose thick and broad, so that the formula of its platy- 
rhine index is higher than in any known race except the Negro ; facial angle compara- 
tively low ; lips thick ; face wide and fleshy ; features coarse and irregular ; average 
stature ranges from 156'2 to 162'1 cm. (5 feet 1 inch to 5 feet 3 inches) ; figure squat ; 
limbs sturdy. The colour of the skin varies from very dark brown to a shade closely 
approaching black. The term Dravidian, as employed by Risley, has a similar mean- 
ing, as regards the tribes which it embraces, to the term Tamulian suggested by 
Mr Hodgson. 

Mr Risley defines also the Aryan type in India, and as by contrast it brings 
out more clearly the Dravidian characters, I append it : — Head relatively long 
(dolichocephalic) ; nose straight, finely cut (leptorhine) ; face long, symmetrically 
narrow ; forehead well developed, features regular ; facial angle high ; stature fairly 
high, ranging from 171 '6 in the Sikhs (5 feet 7 inches) to 165'6 (5 feet 5 inches) 
in the Brahmins of Bengal ; build of figure well proportioned, slender rather than 
massive. The colour of the skin is a very light transparent brown, though with various 
gradations. 

I have had no opportunities of measuring the heads of living natives of India, 
but I propose to summarise the chief characters of the crania measured in Tables 
I.-IV. Unfortunately, some of the tribes are only sparsely represented, as regards 
the number of skulls, but the entire collection gives one a fair amount of material for 
comparison. The Gond, Oraon, Paharia, Karwar, Nagesar, Korwa and Bhuiya 
tribes, who are Dra vidians in the earlier and restricted use of that term, contribute 
collectively fifteen crania.* The Miinda, Bhumij and Turi tribes belong to the old 
Kolarian group, and contribute collectively nineteen specimens.! 

If we take the fifteen skulls in the first or proper Dravidian group, we find that 
the highest length-breadth index was 76*7. In six crania the index was below 70, hyper- 
dolichocephalic ; in five crania it was between 70 and 75, dolichocephalic ; in four crania 
it was between 75 and 76*7, i.e., in the division of the mesaticephalic which approxi- 
mates to the dolichocephalic group.J The customary type was therefore dolichocephalic. 

* I have not included in this number the two Bhima skulls, which possibly may be a sub-division of the Gonds, 
with which, in their form and proportions, they indeed closely correspond. As there may be a doubt as to their racial 
position, I thought it advisable to exclude them. 

t I have not included in this number I.M. No. 407 (Table IV.), which is deformed from scaphocephaly, nor 
I.M. No. 604, Jattia Munda. 

% I have discussed the relations of mesaticephalic skulls to dolichocephalic and brachycephalic crania in Part I. of 
this Memoir in Trans. Roy. Hoc. Edinburgh, vol. xxxix. part iii. p. 744. 



CRANIOLOGY OF PEOPLE OF INDIA. 103 

In the description which I have written of these crania, it is noted that in the 
norma verticalis they were elongated and ovoid ; the sides vertical, or nearly so ; the 
vertex roof-shaped, though not ridged in the sagittal region ; the forehead only slightly 
receding ; the parietooccipital region not flattened, and the occipital squama rounded 
and projecting behind the inion. The muscular ridges and processes were not strong, 
so that the outer table was comparatively smooth, and the skulls were not characterised 
by their weight. 

In nine crania the basi-bregmatic height exceeded the greatest breadth; in four 
the height was less than the breadth ; in two they were equal. In these skulls, as is 
so frequently found in the dolichocephali, the height was usually greater than the 
breadth. 

In the norma facialis the glabella and supra-orbital ridges were not prominent, 
and the nasion was not depressed. In seven specimens the anterior nares were wide 
in relation to their height, and the nasal index was platyrhine ; in six specimens the 
proportion of width was not quite so great and the index was in the mesorhine group, 
but usually in its upper term ; one specimen had a leptorhine index which expressed 
a relatively narrow nose ; the customary type was therefore platyrhine. In seven 
specimens the upper jaw was orthognathous ; in four, in the lower term of the 
mesognathous series ; one specimen only was prognathic ; the customary type of jaw, 
therefore, was orthognathic. In eleven skulls the orbit was microseme ; in one, meso- 
seme ; in three, megaseme ; the orbit was usually low, therefore, in relation to its 
breadth. In the relative proportion of the length and breadth of the palato-alveolar 
arch only one specimen was dolichuranic ; three were mesuranic, seven were brachyuranic ; 
the type form therefore was that of a wide horseshoe. In the determination of the 
length and breadth of the entire face, the lower jaw was present in nine skulls, in seven 
of which the complete facial index was below 90, which places them in the chamse- 
prosopic, or low- faced group, i.e., a face which is broad in relation to its length. 

In Table II. I have given the cranial measurements of two Tamil-speaking male 
natives of Madras, who may be regarded as representing the south Dravidian branch. 
They were both dolichocephalic, and the height exceeded the breadth. The glabella and 
supra-orbital ridges, and the depression at the nasion, were somewhat more pronounced 
than in the skulls of the northern Dravidian tribes. In both, the upper jaw was 
orthognathous, the nose was platyrhine, the orbit was microseme, and the palato- 
alveolar arch in one was mesuranic, in the other brachyuranic. In the skull with a 
lower jaw the face was chamseprosopic. The characters were distinctly Dravidian. 

In the series of seventeen crania under analysis, including the Tamils but excluding 
those marked Kandh, the cubic capacity of thirteen male skulls ranged from 1438 to 
1150 c.c, of which three were above 1400, three were between 1300 and 1400, six were 
between 1200 and 1300, and one was 1150 c.c. ; the mean of the series was 1294 c.c. 
Of the four women, three were between 1200 and 1300, and one was only 1070 ; the 
mean of the series was 1217 c.c. 



104 PROFESSOR SIR W. TURNER ON 

In making this analysis of the crania I have purposely excluded the two marked 
Kandh. In one of these the length-breadth index was 84 # 2, brachycephalic ; in the 
other, 78*5. If the Kandhs are to be regarded as an unmixed Dravidian people, the 
high index in each instance leads one to think that the specimens may have been mis- 
named, and are not genuine examples of the race. If the tribe consists, however, as 
Dalton supposes, of a mixture of races, these crania, more especially the brachycephalic 
specimen, may indicate the presence of a brachycephalic strain, which intermingled with 
the Dravidian would tend to modify the original dolichocephalic type. It should be 
stated that the nasal index in each skull was platyrhine, and in the brachycephalic 
specimen strongly so ; the orbital index was microseme ; the palato-maxillary index 
was brachyuranic ; in neither was the upper jaw prognathic, and in the only one with a 
lower jaw the face was chamseprosopic. In the facial characters the skulls marked 
Kandh corresponded with the Dravidian type. 

We may now proceed to the analysis of the skulls belonging to Kolarian-speaking 
tribes. One specimen, No. 604, Indian museum, marked Jattia Miinda of Bhowro 
village, near Ranchi, had a cephalic index, 80*5, but as in the configuration of the 
cranium it differed so much from the other Miindas I have excluded it from the 
general description. The following observations apply therefore to nineteen skulls. 

In three crania the length-breadth index was below 70, i.e., hyper-dolichocephalic; 
in fourteen specimens it was between 70 and 75, dolichocephalic ; in two specimens, 
between 75 and 76, which, although not numerically, yet in form and essential 
characters were dolichocephalic. In general form, the crania were elongated and ovoid, 
with steep side walls, moderate parietal eminences, no special ridging in the sagittal 
region, and, with the slope outwards to the parietal eminences, not very steep. The 
forehead was not markedly receding, indeed often approaching the vertical ; the parieto- 
occipital slope was gradual ; the occipital squama was, as a rule, rounded, and projected 
behind the inion. The muscular ridges and processes were fairly marked, and the 
skulls had no unusual weight. 

The basi-bregmatic height exceeded the greatest breadth in twelve crania ; it was 
less than the breadth in six, and in one they were equal. 

In the norma facialis the glabella and supra-orbital ridges moderately projected, 
and the nasion was only slightly depressed. In six specimens the anterior nares were 
wide, and the nasal index was platyrhine ; in ten specimens the nose was mesorhine, 
and in all of these, with one exception, with the index above 50 ; two specimens had a 
narrow leptorhine index.* In nine specimens the upper jaw was orthognathous ; eight 
specimens were mesognathous ; no face was prognathous. Ten specimens had a low 
microseme orbit ; four were mesoseme ; four had a high megaseme orbit. In no skull was 
the palato-alveolar arch so elongated as to be dolichuranic ; three were mesuranic ; the 
rest were brachyuranic. The lower jaw was present in eleven of the nineteen skulls, 

* It is not unlikely that in the living person the nose may have, on account of the lateral extension of the alse, a 
more strongly marked platyrhine character than would be obtainable from the width of the anterior nares in the skull itself. 



CRANIOLOGY OF PEOPLE OF INDIA. 105 

in nine of which the proportion of the breadth to the length of the face was low or 
chamseprosopic ; in the remaining two the complete facial index was 90 and 93 
respectively, and the face was within the leptoprosopic division. 

In the Kolarian group the cranial capacity of the men ranged from 1470 to 
1176 c.c. ; of these four were above 1400, five were between 1300 and 1400, six were 
between 1200 and 1300, and one was below 1200 c.c. ; the mean of the series was 1314 c.c. 
The three women's skulls had a mean capacity of 1097 c.c, and the lowest measured 
only 1000 c.c. 

If we compare the characters of the skull in the Dravidian with the Kolarian group, 
we shall find that they correspond in essential particulars. In both, the type of cranium 
in form and proportion was dolichocephalic ; the anterior nares were platyrhine, or in the 
higher term of the mesorhine group ; the presence of a leptorhine index was altogether 
exceptional ; the upper jaw was usually orthognathous ; only one of the thirty-six skulls 
was prognathous ; as a rule the orbit was low or microseme, the palato-alveolar arch was 
brachyuranic. In both groups also the face was chamseprosopic, i.e., the interzygomatic 
width was great in proportion to the length of the face. If we take the cranial capacities 
of the two groups together, the men have a mean 1304 c.c, the women 1157 c.c 

Judging, therefore, from the characters of the skull, one would draw the conclusion 
that there is no difference of moment in the form and proportion of this part of the 
skeleton between the Dravidian and Kolarian types, and support is given to the view 
of their essential structural unity as advocated by Mr Risley. For descriptive pur- 
poses both groups of skulls may be classed therefore as Dravidian. 

Many ethnologists of great eminence have regarded the aborigines of Australia as 
closely associated with the Dravidians of India. Some also consider the Dra vidians to 
be a branch of the great Caucasian stock, and affiliated therefore to Europeans. If 
these two hypotheses are to be regarded as sound, a relationship between the aboriginal 
Australian and the European would be established through the Dravidian people of India. 
The affinities between the Dravidians and Australians have been based upon the 
employment of certain words by both people, apparently derived from common roots ; 
by the use of the boomerang, similar to the well-known Australian weapon, by some 
Dravidian tribes ; by the Indian peninsula having possibly had in a previous geologic 
epoch a land connection with the Austro-Malayan Archipelago, and by certain correspond- 
ences in the physical type of the two people. 

Both Dravidians and Australians have dark skins approximating to black ; dark 
eyes ; black hair, either straight, wavy, or curly, but not woolly or frizzly ; thick lips ; 
low nose with wide nostrils ; usually short stature, though the Australians are some- 
what taller than the Dravidians. 

When the skulls are compared with each other, whilst they correspond in some 
particulars, they differ in others. # In both races the general form and proportions are 

* I may refer to my Challenger Report on Human Crania, part xxix., 1884, for an analysis of the characters of the 
skulls of the Australian aborigines. 



106 PROFESSOR SIR W. TURNER ON 

dolichocephalic, but in the Australians the crania are absolutely longer than in the 
Dravidians, owing in part to the prominence of the glabella. In the Australians it is 
not unusual for the adult male to have the glabello-occipital diameter approaching, 
or even a little more than, 200 mm., whilst in the male Dravidians measured in 
Tables I.-IY, only two specimens reached 191 mm. The Australian skull is heavier, 
and the outer table is coarser and rougher than in the Dravidian ; the forehead also is 
much more receding ; the sagittal region is frequently ridged, and the slope outwards to 
the parietal eminence is steeper. The Australians in the norma facialis have the 
glabella and supra-orbital ridges much more projecting ; the nasion more depressed ; the 
jaws heavier ; the upper jaw usually prognathous, sometimes remarkably so ; the teeth 
larger and coarser, so as to deserve the name macrodont. The coarser character of the 
skull, especially in the temporal region, the heavier jaws and the large strong teeth, 
point to the use of a coarser food by the Australians, for which a more powerful 
masticatory apparatus is required. On the other hand, both Australian and Dravidian 
crania have the nasal index platyrhine or mesorhine ; the occurrence of a long, narrow, 
or leptorhine nose being so exceptional, that its presence indicates that the skull has 
probably been incorrectly named, or is not of a pure race. In both races also the males 
have usually a microseme orbit ; but whilst the Australians have customarily a long 
dolichuranic palato-alveolar arch, in the Dravidians it is broader in relation to the 
length, and frequently brachyuranic. 

As regards the cranial capacity of the Australians, whilst the range in the thirty- 
nine male skulls which I have measured was from 1514 c.c. to 1044, the mean was 
only 1280 c.c, which is somewhat less than the general Dravidian mean 1314 c.c. 
In the female Australians, twenty-four women ranged from 1240 to 930, and 
had a mean 11 15*6 c.c, which is also less than the Dravidian mean 1157 obtained 
from seven female crania. It should be stated that of the series of sixty-three 
Australian skulls, eight men were less than 1200 c.c, and only four above 1400 
c.c. ; whilst of the women only three were above 1200 c.c, and ten were below 
1100 c.c. 

By a careful comparison of Australian and Dravidian crania, there ought not to 
be much difficulty in distinguishing one from the other. The comparative study of the 
characters of the two series of crania has not led me to the conclusion that they can be 
adduced in support of the theory of the unity of the two people. 

The skulls which belonged to the Koydwar, Kamar, Ahir-Goala and Teli castes or 
tribes were dolichocephalic, platyrhine, and, with one exception, orthognathic, characters 
which they shared with the Dravidian crania. It is not unlikely that in these castes 
there is a strong Dravidian element. The Bhima skulls, though dolichocephalic and 
either orthognathous or mesognathous, were not platyrhine. The Bunjana skull, on the 
other hand, was hyper-brachycephalic, though the jaw was orthognathous, and the nose 
was platyrhine. The Lohar skull was mesaticephalic and orthognathic, but the nasal 
index was leptorhine, and in so far pointed to a predominance of Aryan blood. The 



CRANIOLOGY OF PEOPLE OF INDIA. 107 

specimens were too few to enable one to draw a general conclusion on the cranial 
characters of these tribes or castes. 

As already stated, the skulls of the Uriya group presented considerable variations in 
the cephalic index, and in the configuration of the skull. In the dolichocephalic series 
about one-third were platyrhine in the nasal index, the others were mesorhine or 
leptorhine ; in the majority the upper jaw was orthognathous, and no skull was 
prognathous. In the mesaticephalic series the majority were mesorhine, only two were 
platyrhine, and one was leptorhine ; the upper jaw was usually orthognathous, and only 
one was prognathous. The brachycephalic series was represented by only five speci- 
mens, three of which were mesorhine, one platyrhine, and one leptorhine ; as regards 
the upper jaw, no specimen was prognathous. 

As many of these crania were derived by the Indian Museum from the Medical 
School in Calcutta, it may have happened that no proper history of the dead had been 
obtained, and that, in consequence, the skulls had not been accurately identified. # If 
we grant that they had all belonged to the Uriya-speaking people, the inference seems 
obvious that the community of language would by no means express unity of race. 

It would seem, therefore, that in the Uriyas some crania partook of Dravidian, 
others of Aryan characters, and from the presence of a proportion of brachycephalic 
skulls, there might also have been a trace of Mongolian or other brachycephalic 
intermixture. As regards the Uriya group, it is probable that a considerable Dravidian 
element is contributed through the presence of tribes of Hinduised aborigines, inter- 
mingled with the people who possess a strain of Aryan blood. 

I will now proceed to the consideration of the Veddahs, the aboriginal hill tribe 
in Ceylon, of the Mincopies, the aborigines in the Andaman Islands, and of the hill 
tribes in the Malay peninsula. 

Veddahs. Table IX. 

In the study of the aboriginal dolichocephalic tribes in and near the Indian peninsula, 
we should not overlook the aborigines known as Veddahs or Weddas, who live in 
the hill districts of the adjoining island of Ceylon. Various travellers in Ceylon, 
of whom may be especially mentioned Robert KNOX,t John Davy,J C. Pridham,§ 
Sir Emerson Tennent,|| B. F. HartshorneJ John Bailey, ## and C. S. V. Stevens, ft 
have given accounts of these people and the districts in which they live. George 

* The crania marked Uriya, Orissa, in the Tables, are those which had been obtained from the Medical College. 
It will be seen that specimens so marked occur in each of the three groups tabulated in VI., VII., VIII. 

t Historical Relation of the Island of Ceylon. London, 1817. 

% Account of the Interior of Ceylon and of its Inhabitants. London, 1821. 

§ Ceylon and its Dependencies. London, 1849. \\ Ceylon. London, 1859. 

IT Fortnightly Review, London, 1876, vol. xix. 
** Trans. Ethnol. Soc, London, 1863. 
tt Overland Times of Ceylon, Nov. 6th, 1886. 

VOL. XL. PART I. (NO. 6). Q 



108 PROFESSOR SIR W. TURNER ON 

Busk described four specimens of their crania in 1862,* which, along with three 
others, had their chief measurements recorded by Sir Wm. Flower in his catalogue 
of crania in the Hunterian Museum. MM. De Quatrefages and Hamy figured 
a skull in the Crania Ethnica, PI. LVIII. Barnard Davis has also recorded, 
in the Thesaurus CraniorumJ the measures of ten Veddah skulls. George 
Rolleston exhibited to the British Association in 1872 1 photographs of jungle 
Veddahs, and also three skulls of this people in the Oxford Museum. Virchow has 
described § three Veddah skulls, and has discussed the ethnological relations of the 
people. Arthur Thomson has given an account || of the osteology of the Veddahs, 
and has described, along with the other bones of the skeleton, the characters of nine 
skulls in the Oxford Museum. He has also included in his tables of measurement 
three skulls measured by Virchow, fifteen in the Museum of the Royal College of 
Surgeons of England, and eleven in the collection of Barnard Davis. Much the 
most complete description of the habits, distribution, and physical characters of the 
Veddahs, and, indeed, of the natives generally of Ceylon, is contained in the 
monumental work on that island by Paul and Fritz Sarasin,! who record, in addition 
to an account of the skeleton generally, the measurements of eighteen male and four 
female skulls from the interior of the island, and four male and four female skulls from 
the coast districts ; also some young and imperfect crania. 

As regards the external physical characters of the Veddahs, the Sarasins have 
contributed the fullest and most carefully analytical description, which I have 
summarised as follows : — The colour of the face in men varies from a deep brown to 
one with shades of lighter brown ; they have never seen a pure black skin, and those 
that seem to be black, when closely examined are distinctly brown. The skin of the 
breast is more frequently an opaque brown, though it may have a medium or reddish- 
brown shade. In women there is not the same range in the brown tint, and on the 
whole the skin is a clearer brown. The eyes have a brownish-black or opaque brown 
colour. The hair of the head is black, coarse, wavy, tangled, and hanging down 
to the shoulders or the back ; that of the beard and moustache is black and sparse. 
On the body the hair is also sparse, though on the legs it may be abundant. 
The face is tolerably broad and not high, the mean index of sixteen men being 80*7, 
i.e., low-faced, chamseprosopic : the chin is pointed. The eyebrows are not strong, the 
eyes are generally large, and there is no fold of skin connecting the eyelids at the 
inner canthus (epikanthus), as in the Mongols. The nose has a deep pit in men at 
the root, the bridge is not strong, and the alee have considerable breadth; in women 
the nose is flatter than in men. The lips are large and the jaws are orthognathic. 

* Proc. Linn. Soc, 1862, vol. vi. 
t Thesaurus Craniorum, 1867. 

| -Scientific Papers and Addresses, vol. i., Oxford, 1884, edited by W. Turner. 
§ " Ueber die Weddas von Ceylon," Abh. der K. Akad. der Wiss. zu Berlin, 1881. 
|| Journ. Anth. Inst., Nov. 1889. 
IT ErgebnissenaturuissenschaftlicherForschungen auf Ceylon, 3d Band, die TVeddas von Ceylon. Wiesbaden, 1892-93. 



CRANIOLOGY OF PEOPLE OF INDIA. 109 

The stature is low; in the Veddahs of the central district, where the race is probably the 
purest, the mean height of twenty-four men was 1533 mm. (5 feet J inch), of eleven 
women 1433 mm. (4 feet 7 inches) ; that of twenty-four men from the coast district was 
1588 mm. (5 feet 2 inches), of ten women 1494 mm. (4 feet 9 inches), whilst fourteen 
men from the district of Wewatte were 1607 mm. (5 feet 2f inches) in height. In the 
sea-coast and Wewatte districts there has probably been some intermixture with 
Singhalese, Tamils, or even Indo-Arabians, which would affect both the stature and other 
physical characters of the Veddahs. 

As regards the Dravidian Tamils of Ceylon, the Sarasins have also described their 
external physical characters. They are a bigger people than the Veddahs ; the mean 
stature of the men was 1653 mm. (5 feet 4 inches) and of the women 1545 mm. 
(5 feet § inch). The pigmentation of the skin was deeper in the lower than the higher 
castes. In about one-half the men examined the skin of the face" was a medium, rarely 
a red-tinted, brown ; in the other half a brighter brown shading into yellow : in the 
women a more opaque brown prevailed. The eyes were an opaque brown. The hair 
was black and scarcely differed from the hair of the Veddahs, though it was perhaps 
coarser and had a greater tendency to curl. The supra-orbital region was often well 
developed in the men. The face was oval and proportionately higher and narrower 
than in the Veddahs. The eyes were large and without an epikanthus. The nose had 
a stronger bridge than in the Veddahs, and the alas were not so wide. The lips were 
thick. The teeth were strongly developed, and the jaws were more projecting than in 
the Veddahs. 

I have examined and measured nine Veddah crania which have not previously been 
described. Three of these belonged to the Henderson Trust Collection, now in the 
Edinburgh University Museum; they were presented in 1827 by the Rev. G. Lyon 
and were probably the earliest examples of the race to reach this country. One was 
presented to me about twenty years ago by the late Dr Kriekenbeck of Colombo ; the 
man had died in jail ; the skull is metopic, a rare condition in dolichocephalic savages. 
One from Batticaloa, in the east of Ceylon, was presented by H. Thwaites, Esq. In one 
skull, No. 555 in the Indian Museum, the face was broken. Of the three others, two 
have been for some years in the Museum of Trinity College, Dublin, and another, also 
in Dublin, came from Batticaloa. I have to thank Professor Cunningham for per- 
mission to examine them. The skulls were all adults ; to all appearance seven were 
men and two probably women. 

When examined in the norma verticalis the crania were seen to be elongated 
antero-posteriorly ; the side walls were almost vertical ; the vertex in some specimens 
was roof-shaped, but not keeled in the sagittal region, and in others the vertex was 
more flattened; the parietal eminences were distinct. The skull sloped gently 
backwards as a rule into the occipital region, and the occipital point usually 
projected definitely behind the inion ; there was no evidence of parieto-occipital 
flattening. In three of the skulls the length-breadth index ranged from 66*5 to 



110 



PROFESSOR SIR W. TURNER ON 



Table IX. 
Veddah. 





Henderson Trust. 


E.U.A 


M. 


I.M. 


Trinity College, Dublin. 


Collection number, . 


143 


145 


144 


Batticaloa. 


Me topic. 


555 






Batticaloa. 


Age, 


Ad. 


Ad. 


Ad. 


Ad. 


Ad. 


Ad. 


Ad. 


Ad. 


Ad. 


Sex, ..... 


M. 


M. 


F. 


M. 


M. 


M. 


M. 


M. 


F. 


Cubic capacity, 




1226 


1090 


1090 


1100 


1170 


1262 


1362 


1088 


Glabello-occipital length, . 


17 Tap. 


170 


174 


167 


180 


180 


175 


185 


174 


Basi-bregmatic height, . 


130 


129 


131 


127 


126 


130 


137 


139 


127 


Vertical Index, 


7S-Jf 


75-9 


75-8 


76' 


70' 


72' 


78' 


75' 


73- 


Minimum frontal diameter, 


93 


87 


88 


93 


93 


91 


93 


94 


89 


Stephanie, .... 


108 


104 


100 


98 


99 


96 


109 


113 


100 


Asterionic, .... 


103 


98 


99 


97 


100 


103 


98 


101 


101 


Greatest parieto - squamous 




















breadth, .... 


125ap. 


128s. 


121p. 


127s. 


121s. 


128s. 


125s. 


123s. 


127s. 


Cephalic Index, 


70-6 


75-8 


69-5 


76- 


67' 


71' 


71'J,. 


66-5 


73' 


Horizontal circumference, 


492ap. 


478 


475 


477 


500 


497 


490 


510 


485 


Frontal longitudinal arc, . 




123 


120 


120 


120 


130 


130 


132 


120 


Parietal „ „ , 


130 ( 


233 


128 


111 


130 


128 


122 


145 


110 


Occipital ,, ,, . 


104 j 


105 


110 


113 


114 


112 


110 


113 


Total „ „ . 


• • • 


356 


353 


341 


363 


372 


364 


387 


343 


Vertical transverse arc, 


292 


288 


281 


289 


278 


292 


295 


302 


288 


Length of foramen magnum, 


37 


34 


33 


32 


29 


35 


34 


33 


32 


Basi-nasal length, 


94 


91 


97 


97 


98 


96 


97 


101 


100 


Basi-alveolar length, 


96 


89 


88 


98 


100 


• • • 


92ap. 


90ap. 


93 


Gnathic Index, 


102-1 


97-8 


90-7 


101- 


102' 






94'8 


89' 


93' 


Interzygomatic breadth, . 


131 


120 


111 


129 


121 






126 


117 


123 


Intermalar ,, 


117 


109 


103 


116 


116 






112 


108 


113 


Nasio-mental length, 






• • ■ 


107 


117 






• • • 


• • • 




Nasio-alveolar ,, . . 


59 


56 


55 


66 


64 






52 


60 


58 


Complete Facial Index, . 








82-9 


96-7 




., 




... 




Nasal height, .... 


43 


44 


42 


45 


46 






42 


45 


44 


Nasal width, .... 


25 


23 


26ap. 


22 


22 






25 


23 


25 


Nasal Index, .... 


58-1 


52-8 


61-9 


48-9 


47-8 






59-5 


51' 


56-8 


Orbital width, 


41 


36 


37 


38 


36 


36 


39 


38 


35 


Orbital height, 


29 


30 


32 


31 


30 


30 


31 


34 


33 


Orbital Index, 


70-7 


83-3 


86-5 


81-6 


83' 


83' 


79-5 


89-5 


94-3 


Palato-maxillary length, . 


50 


50 


47 


54 


54 






52 


45ap. 


50 


Palato-maxillary breadth, 


66 


58 


53 


64 


63 




, , 


56 


57 


63 


Palato-maxillary Index, . 


132- 


116- 


112-7 


118-5 


116-6 






107-9 


126-6 


126' 




r Symphysial height, 






... 


28 


33 








• •• 




c3 


Coronoid „ 


... 






65 


61 








... 


58 


<u 1 


Condyloid „ 


... 






59 


61 








... 


48 


Gonio-symphysial length, . 








90 


95 






• • • 


... 


88 


o 
h3 


Inter-gonial width, 


• , . 




... 


82 


82 




1 1 




... 


80 


Breadth of ascending ramus, 


... 






33 


34 




■■ 




... 


39 



CRANIOLOGY OF PEOPLE OF INDIA. Ill 

69*5, hyperdolichocephalic ; in four the index was from 70'6 to 73, dolichocephalic; 
in the remaining two it was 75*3 and 76. The mean of the series was 71*1- 
In seven skulls the basi-bregmatic diameter exceeded the greatest breadth ; in two 
they were equal : the mean vertical index of the series was 74 '3. In one skull 
the occipital longitudinal arc was a little longer than the parietal, but not so long as 
the frontal arc ; in four skulls the frontal arc exceeded the parietal ; in three the 
opposite condition was seen. With one exception the crania were cryptozygous. 

When looked at in the norma lateralis, the glabella and supra-orbital ridges pro- 
jected only slightly, the forehead was sometimes nearly vertical, at others receded a 
little. The nasion was depressed in one specimen, but not in the others. The nasal 
bones were usually small, not prominent and concave forwards. The nasal spine of the 
superior maxillae was distinct, and the floor of the nose was separated from the incisive 
region by a ridge. The mean nasal index was 54*4 platyrhine, and of the individual 
skulls four were markedly platyrhine, three were mesorhine, and one on the boundary 
between leptorhine and mesorhine. The orbits varied in the relation of width and 
height ; six were low, microsome ; two were high, megaseme ; one was mesoseme ; the 
mean index, 83*5, was microseme. In no specimen was the upper jaw prognathous, 
five were orthognathous, and three were mesognathous ; the mean gnathic index, 96*3, 
was orthognathous. 

The nasio-mental diameter could be measured in only two skulls, in one of which the 
complete facial index was chamseprosopic, in the other high-faced or leptoprosopic. The 
mean palato-maxillary index was 119*5, i.e., brachyuranic, and with two exceptions, one 
dolichuranic, the other mesuranic, the other skulls belonged to the brachyuranic group. 

The teeth had been fully erupted in all the skulls except a wisdom tooth in No. 
143 ; the crowns were mostly betel stained, and the grinding surfaces of the molars 
were worn flat. The sutures were, as a rule, distinct, and one was metopic ; though in 
one the sagittal was partially obliterated. In two crania the lambdoidal suture contained 
small Wormian bones. One had a right epipteric bone, but in none was the squamous 
temporal in articulation with the frontal. 

The cranial capacity in both sexes was low, the mean of six men was only 
1201 c.c, and the range was from 1090 to 1362 c.c. ; the mean of two women was 
only 1089 c.c. The lower jaw w 7 as present in only three specimens, in each of which 
the chin was well marked ; the body of the bone was deep, for the lodgment of the fangs 
of the teeth and the angle was well marked. 

I may now briefly state the chief cranial characters of the specimens described by 
previous observers. Arthur Thomson has embodied in a table the measurements 
made by Busk, Virchow, Flower, Barnard Davis, and himself. Of the thirty-seven 
skulls included in that table fourteen had a length-breadth index below 70, fourteen 
were between 70 and 75, five were from 75 to 77*5, one was 78, and three w r ere from 
80*6 to 82*9. All the skulls, with four exceptions, were definitely dolichocephalic or 
in the lower terms of the mesaticephalic group. Of the four exceptional specimens, 



112 PROFESSOR SIR W. TURNER ON 

one with the index 82 "9 from Bintenne of Badulla (R.C.S. Eng. No. 676) is said to be 
unsymmetrically distorted from occipital pressure, which had doubtless affected the 
relation of length to breadth ; another, from Batticaloa, measured by Virchow, with an 
index 80 '6, is said to be evidently abnormal, probably from an artificial or accidental 
deformity in the occipital region. 

This series of skulls confirms what I have previously had occasion to point out in 
the study of crania, that in the dolichocephalic crania of savage races the basi-bregmatic 
height usualty exceeds the greatest breadth. Thus, of thirty-six skulls in Thomson's 
table, in which both breadth and height are recorded, the height exceeded the breadth 
in thirty-one, and it was equal to the breadth in one specimen. In only four crania 
was the height less than the breadth, and in three of these the length-breadth index 
was above 80, and the skull was brachy cephalic. 

The seventeen skulls in Thomson's table in which the proportions of the upper jaws 
were measured were all orthognathous. Of the twenty-two skulls in which the pro- 
portions of the nose were measured, ten were platyrhine, seven were mesorhine, and 
only five were leptorhine. The orbital index was variable ; in six specimens it was 
microseme, in eight mesoseme, in eight megaseme. The palato-alveolar index in eight 
skulls measured exceeded 120 in only one specimen. 

As regards the cranial capacity it is difficult to make a precise statement, as the 
methods used by different observers in its determination were not uniform, and the 
results cannot be strictly compared with each other. It may suffice to state that the 
capacity in one woman's skull is said to be as low as 960 c.c. ; in eleven other women 
the range of capacity was 1025 to 1442 c.c, and the mean was 1230 c.c., i.e., micro- 
cephalic. In twenty men the range was from 1140 to 1611 and the mean was 1336 c.c, 
also microcephalic In both sexes the mean was materially higher than in the skulls 
which I measured, and several skulls exceeded considerably that with the highest 
capacity, 1362 c.c. in my series, an excess which may perhaps partly be due to the 
methods employed yielding a larger result than is obtained by the plan which I am in 
the habit of following, which I believe to be more exact.* 

If we now examine the series of thirty skulls measured by the Messrs Sarasin, we 
find that the mean length-breadth index of the Veddahs from the interior was 70 '5 for 
seventeen men, and 69"1 for four women ; whilst the corresponding index of four men 
from the coast was 76*5, and of four women 73. No skull was brachycephalic, but in 
five the index was from 75 "9 to 79*8. In each group, except in that of the men from the 
coast, the height exceeded the breadth. The mean complete facial index in each group 
was near the upper limit of the chamseprosopic division. The mean gnathic index in each 
group was orthognathous, and no specimen was prognathous, and only a small minority 
was mesognathous. The mean nasal index was in the higher mesorhine series ; only 
four specimens were leptorhine, but thirteen were platyrhine. Fifteen specimens were 

* I have described my method in Cludlemjer Reports, part xxix. p. 3, 1884. By the method of Bkoca, followed 
l>y so many craniologists, the capacity is overstated. 



ORANIOLOGY OF PEOPLE OF INDIA. 113 

megaseme, and the mean orbital index of the series came just within the megaseme 
division, but four specimens were microseme. In the relative proportions of the length 
and breadth of the palato-alveolar arch the mean index fell just within the brachy- 
uranic division. As regards the cranial capacity, the mean of twenty-two men was 
1277 c.c, and of ten women 1139 c.c. 

Seventy-six skulls ascribed to Veddahs have now been studied and described by 
experienced craniologists. With very few exceptions they were elongated, with the 
sides approaching the vertical, the sagittal line not keeled, or only slightly so ; rela- 
tively narrow, and the length-breadth index was dolichocephalic, frequently hyper- 
dolichocephalic. It is known that some of the skulls in which the index exceeded 75 
or 76 were from natives who had lived on the coast, where the possibility of an 
admixture of blood with other races is probable. The basi-bregmatic height in 
almost every case exceeded the greatest breadth. 

The face was broad in relation to the height. The nose was platyrhine or mesorhine, 
seldom leptorhine. The upper jaw was orthognathous. The orbit was variable in the 
proportions of height and breadth, but tended to a relatively high vertical diameter. 
The palato-alveolar arch was moderately elongated. The cranial capacity was low. 

If these characters be compared with those previously given, as found in the 
Dravidian group, they will be found to correspond in many respects. In both the 
crania were dolichocephalic in form and proportions ; in both the height as a rule 
exceeded the breadth. The glabella and supra-orbital ridges did not strongly project, 
the forehead was not specially retreating, and in many specimens approached the 
vertical ; the occipital squama was usually convex, and projected behind the inion. 
The face was low in relation to the breadth ; the nasion was seldom much depressed ; 
the anterior nares were platyrhine or mesorhine, rarely leptorhine ; the upper jaw was 
orthognathous, occasionally mesognathous, not prognathous ; the orbits varied in the 
proportion of width and height ; the palato-alveolar arch also varied, though the index 
seldom much exceeded 120, and the breadth was not greatly in excess of the length. 
The cranial capacity was microcephalic in both Veddahs and Dravidian s, though the 
former were, on the whole, of smaller capacity than the latter. It is difficult, therefore, 
to lay down a series of characters in which the Veddah and Dravidian skulls differed 
from each other. 

Andaman Islanders. Table X. 

I have stated on p. 101 that the possibility of the presence of a Negrito element in 
the people of India has to be enquired into. Considerable attention has been given to 
this subject by several ethnologists, and opinions both affirmative of and adverse to the 
affinity between the black races of India and the Negritos have been expressed. Mr 
O'Donnell in his Census Report has indeed used the term Negritic as if it were 
synonymous with Dravidian, and has indicated (p. 264) a route along which he thinks a 



114 PROFESSOR SIR W. TURNER ON 

Negrito race could have reached southern India and passed to south-eastern Asia and 
Australia. 

That a Negrito race is scattered in the Philippine Islands is well established, and 
that similar people exist in other islands of the great eastern Archipelago, and in a few 
localities on the adjacent continent, has been asserted by eminent authorities. There 
can be no doubt that the Mincopies, or natives of the Andaman Islands in the Bay of 
Bengal, have the Negrito characters of low stature, very dark skin approaching black, 
with woolly or frizzly black hair growing in short, close curls. The proximhty of these 
islands to the Indian peninsula has seemed to indicate that a Negrito population had 
preceded in India the present dark-skinned Dravidian race, and that traces of their 
existence can be still found in the aboriginal people. Although some writers have 
referred to black, frizzly or woolly-haired tribes in certain of the mountainous districts 
in India, the evidence on this head is by no means conclusive, and it may be a question 
if the terms woolly or frizzly may not have been loosely used to characterise the wavy 
hair which has been seen in individuals of some of the aboriginal tribes. The statements 
which have been made in regard to this question have been carefully analysed by A. B. 
Meyer, in his Memoir on the Distribution of the Negritos* and he has come to the 
conclusion that the present state of our knowledge does not permit a judgment to be 
given that the aboriginal people of India were Negritos. As bearing on this matter, I 
may state that Dalton, in his Ethnology of Bengal, figures a Santal with curly hair, 
quite distinct, however, from the short, close locks of the natives of the Andaman Islands. 
In his portraits of the Juangs and Korwas, two tribes short in stature and primitive in 
habits, the hair is long, more or less matted, but not curly. Messrs Forbes Watson 
and Sir J. W. Kaye have reproduced f photographs of a Santal, Kurumbas, Yenadies, 
a jungle tribe of Chingleput, a Toda and a Kandh with curly tangled hair. Edgar 
Thurston, in his description of the short, broad-nosed tribes of Southern India, figures 
Kadirs from the Anaimalai Hills, in whom the hair was curly, relatively long, and 
projecting from the head, not unlike the " mop " of the Papuans. He also gives 
portraits of Paniyans from Malabar and Kurumbas from the Nilgiri Hills, in whom the 
hair had a similar character. These tribes or races are primitive in their habits, and the 
stature does not apparently exceed 5 feet 2 inches. Wavy and curly black hair are, 
he says, in the south Dravidians common types ; but he had seen no head of hair to 
which the term woolly could be correctly applied.^ The wavy or curly character seems 
to be no more marked than the curly locks not unfrequently seen in the white races. 

I need not dwell upon the physical characters and the customs of the people of the 
Andaman Islands, as they have been described in considerable detail by J. Mouat,§ 
E. H. Man, || de Quatrefages,1F and E. S. Brander. ## 

* Dresden, 1899. + The People of India, 10 vols., 1868, e. s. London. India Museum. 

X Madras Bulletin, vol. ii. No. 3, p. 187, 1899. § Adventures in Andaman Islands. London, 1861. 

|| Journ. Anihrop. Inst., xiv., 1885. 

T Les Pygmies, Paris, 1887 ; and in conjunction with M. Hamy, Crania Ethnica, p. 184. 
** Proc. Roy. Soc. Edin., 1880, p. 415. 



CRANIOLOGY OF PEOPLE OF INDIA. 115 

The University Anatomical Museum contains the skulls of six Andaman Islanders, 
presented, along with other bones of the skeleton, by Drs J. Dougal, J. S. Forrester, 
D. D. Cunningham, and Colonel Cadell, V.C. In the Museum of the Royal College of 
Surgeons of Edinburgh is another skeleton.* Of the seven skulls, two had not quite 
reached maturity ; the others were adult, of these three apparently were women and 
two men. 

When looked at in the norma verticalis the skulls were seen to be flattened at the 
vertex, and the vault had a low curve ; they were relatively wider in the parietal 
regions, the eminences in which were distinctly marked even in the men's skulls. The 
Stephanie diameter was much below the parietal, and its relatively short breadth contri- 
buted to give a characteristic contour to the cranium. Although there was no appearance 
of parieto-occipital flattening, the slope behind the obelion was somewhat abrupt, and the 
parietal eminences were much closer to the occipital than to the frontal pole of the cranium. 
With one exception the skulls were cryptozygous. The crania ranged in length from 
173 to 158 mm., in greatest breadth from 141 to 128 mm. The mean length-breadth 
index was 81*5, brachycephalic, and the range was from 78*6 to 887. In each skull 
the basi-bregmatic height was, as is customary in brachycephalic crania, distinctly less 
than the greatest breadth, and the mean vertical index was 757. With one excep- 
tion the occipital longitudinal arc was the shortest, but there was no constancy in 
the relative proportions of the frontal and parietal arcs. 

In the norma lateralis the glabella and supra- orbital ridges were feeble in the 
males and scarcely marked in the female skulls ; the forehead was vertical in the 
women and very slightly receding in the men ; the frontal eminences were distinct. 
The nasion was not depressed, the nasal bones were not prominent except in one 
specimen, and were flattened across the bridge. In two skulls the nasal index was 
mesorhine, the rest were platyrhine, and the mean index was 55. One orbit was high 
in relation to the width, three were much lower, and the others were intermediate, the 
mean index of the series, 8 5 "5, was mesorhine. The upper jaw in its degree of projection 
was in two cases orthognathous, in one prognathous, in the rest mesognathous, the mean 
of the series was 99*8, mesognathous. The face in each specimen was chamaeprosopic, 
and the mean complete facial index was 80'5. 

The nasal spine of the superior maxillae was moderate, and the floor of the nose was 
usually separated from the incisive region by a ridge. The teeth had mostly erupted, 
but in some of the specimens the wisdoms were not complete, and in one of these the 
right upper canine and right lower central incisor were concealed in the jaws. In the 
older skulls the crowns were worn from use. In the younger skulls the sutures were 
well denticulated, but in the older they were beginning to be obliterated. One was 
metopic, and in it the frontal transverse diameters much exceeded those in the other 
skulls. In one specimen a large Wormian bone constituted the upper part of the 

* The bones of five of the skeletons, exclusive of the skulls, were described by me in the Challenger Reports, Zoology, 
vol. xvi. part xlvii., 1886. 

VOL. XL. PART I. (NO. 6). R 



116 



PROFESSOR SIR W. TURNER ON 



Table X. 



Andaman Islanders — Sakai. 







Andaman Islanders. 




Sakai. 








Edin. 


Univ. Anat. Museum. 




E.R.C.S. 


Ed. U. 


A. M. 




















Kampar. 


Pahang. 






Collection number, . 


No. 6 


No. 1 


No. 5 


No. 2 


No. 3 


No. 4 














Age, .... 


Ad. 


21 ? 


Ad. 


Ad. 


Ad. 


23? 


Ad. 




Ad. 


Ad. 






Sex, .... 


M. 


M. 


M. 


F. 


F. 


F. 


F. 




M. 


M. 






Cubic capacity, 


1080 


1255 


1270 


1080 


1190 


1153 


1090 




1155 


1385 






Glabello-occipital length, . 


158 


159 


173 


166 


161 


159 


164 




169 


175 






Basi-bregmatic height, 


125 


123 


127 


122 


119 


125 


121 




130ap. 


134 






Vertical Index, 


79-1 


77'4 


73-4 


73-5 


73-9 


78-6 


73-8 




76-5 


76-6 






Minimum frontal diameter, 


89 


90 


102 


90 


88 


90 


87 




91 


94 






Stephanie, 


100 


111 


122 


107 


104 


109 


99 




95 


106 






Asterionic, 


97 


102 


96 


99 


95 


97 


91 




99 


106 






Greatest parieto-squamous 


























breadth, 


128p. 


141p. 


136p. 


131p. 


130s. 


131 p. 


132p. 




126s. 


139s. 






Cephalic Index, 


81- 


88-7 


78-6 


78-9 


80-7 


82-4 


80-5 




74-6 


79-4 






Horizontal circumference, . 


462 


468 


493 


475 


468 


465 


467 




473 


505 






Frontal-longitudinal arc, . 


115 


113 


123 


111 


121 


117 


112 




112 


120 






Parietal „ ,, 


115 


102 


135 


113 


113 


120 


125 




127 


128 






Occipital ,, „ 


102 




103 


111 


103 


100 


101 




108 


111 






Total ,, ,, 


332 


345 


361 


335 


337 


337 


338 




347 


359 






Vertical transverse arc, 


288 


300 


304 


291 


288 


295 


270 




276 


295 






Length of foramen magnum, 


29 


31 


32 


33 


29 


34 


30 




36 


37 






Basi-nasal length, 


90 


83 


94 


93 


90 


89 


92 




93 


98 






Basi-alveolar length, . 


91 


82 


91 


90 


91 


89 


96 




89 


93ap 






Gnathic Index, 


101-1 


98-8 


96-8 


96-8 


101-1 


100- 


104-3 




95-7 


94-9 


ap 




Interzygomatic breadth, . 


121 


112 


128 


123 


118 


115 


119 




116 








Intermalar breadth, . 


113 


103 


118 


112 


106 


103 


111 




108 








Nasio-mental length, 


99 


92 


103 


96 


88 


92 


■ •• 












Nasio-alveolar ,, 


58 


53 


62 


59 


54 


55 


56 




40 








Complete Facial Index, 


82- 


82-1 


80-4 


78' 


74-5 


80- 


... 












Nasal height, . 


43 


40 


45 


43 


41 


41 


44 




41 


51 






Nasal width, . ' . 


22 


20 


24 


25 


21 


23 


25 




24 


26 






Nasal Index, . 


51-2 


so- 


53S 


58-1 


51-2 


56-1 


56-8 




58-5 


51- 






Orbital width, . 


37 


35 


37 


36 


37 


37 


36 




36 








Orbital height, . 


32 


32 


32 


30 


30 


31 


31 




28 








Orbital Index, . 


86-5 


91 -4 


86-5 


83-3 


81-1 


83-8 


86-1 




78- 








Palato-maxillary length, . 


50 


47 


50 


52 


49 


50 


53 




47 








Palato-maxillary breadth, . 


62 


56 


64 


60 


53 


56 


59 




59 








Palato-maxillary Index, . 


12£ 


119-1 


128- 


115-4 


108-1 


112- 


111-3 




125- 










' Symphysial height, . 


26 


22 


23 


23 


23 


25 


24 




... 










Coronoid „ 


59 


49 


49 


53 


53 


51 


55 












i- 


Condyloid ,, 


54 


53 


51 


52 


47 


47 


51 












08 


Gonio-symphysial 


























® 


length, . 


85 


77 


91 


85 


85 


80 


89 












q 


Inter-gonial width, . 


85 


80 


94 


82 


76 


78 


84 




. . . 








>-H 


Breadth of ascending 




























ramus, . 


31 


27 


35 


34 


37 


36 


35 


















Metopic 





















CRANIOLOGY OF PEOPLE OF INDIA. 117 

occipital squama. One skull had an epipteric bone on each side ; another had on the 
left side a broad articulation of the squamous temporal with the frontal, and on the right 
both an epipteric bone and a direct temporo-frontal articulation. In one the os planum 
of the ethmoid was so narrowed in front that the orbital plate of the maxilla almost 
articulated with the frontal ; this specimen approached therefore the condition of direct 
fronto-maxillary articulation, such as I have previously referred to on page 94. 
In three skulls indications of an infra-orbital suture were present. The lower 
jaw had a feeble chin and shallow symphysis, the vertical diameter of the body of 
the bone was moderate, the coronoid process was short, and the sigmoid notch 
shallow. The cubic capacity of the crania was small ; the males ranged from 1080 
to 1270, with a mean 1202 c.c. : the females from 1080 to 1153, with a mean of 
1106 c.c. 

Although Owen and Busk had described a few crania, the late Sir Wm. Flower 
made the most extensive research into the characters of the Andaman skull that has 
yet been conducted. He described* a series forty-eight in number, six of which 
were metopic, and as one of my specimens had the same character, it is obvious 
that a persistent frontal suture is not uncommon in the crania of this race. The 
mean length-breadth index of his specimens was 82 '8. The height was less than 
the breadth, and the length-height index was 77 '7. The mean gnathic index was 
100 in the men, 102 in the women. The mean nasal index was 51*1, and the 
orbital index, though variable, had a mean 90*9. Both in Flower's series and in 
mine the length-breadth index was brachy cephalic ; the height was distinctly below 
the breadth ; the upper jaw was mesognathous ; the nasal index was mesorhine 
or platyrhine ; the orbits were mesoseme or megaseme ; the cranial capacity was 
microcephalic. The number of specimens examined is so large as to justify one 
in saying that the leading characters of the cranium in these people have now been 
ascertained. 

The series of Dravidian crania described in this Memoir differ in essential particulars 
from those of the Andaman Islanders, and the eye at once recognises the differential 
features, both in form and proportion. The measurements made by Mr Thurston of the 
heads of the hill tribes in the Madras Presidency have shown the great majority to have 
a length-breadth index below 75, though a few ranged from 75 to 77*5; the south 
Dra vidians, like those further north, have, therefore, heads of dolichocephalic proportions. 
Did we accept the view that a brachy cephalic Negrito people preceded the Dravidians 
in the occupation of India, we could not, I consider, regard the latter, either in cranial 
configuration or external physical characters, as the direct descendants of the former. 
It might be argued that had there been a previous Negrito people, some amount of 
intermixture in times past of the two races might have taken place, which might have 
led to the production of a wavy or curly character of the hair such as has been seen in 
the tribes referred to on p. 114, and to the occasional presence of a skull tending to 

* Joum. Anthrop. Inst., Nov. 1879, vol. ix., and Nov. 1884. 



118 PROFESSOR SIR W. TURNER ON 

brachycephalic proportions in some of the existing aboriginal Dravidian tribes, but the 
direct evidence of either a past or a present Negrito population in India has yet to be 
obtained.* 

Sakai. Table X. 

The name Sakai is given to aboriginal people dwelling in the hill regions in the 
Malay peninsula. Since the early part of the century certain tribes called Semangs 
have been described in Kedah to the north of Pinang and in Tringanu on the east coast. 
Anderson speaks of a native of Kedah as 4 ft. 6 in. in height, the hair woolly and 
tufted, the skin jet black, the lips thick, the nose flat, the belly protuberant as in the 
Andaman Islanders. J. R. Logan states that a tribe of Semangs in the hills opposite 
Pinang have a stature from 4 ft. 8 in. to 4 ft. 10 in., the nose with depressed root and 
spreading alas, the skin dark brown though sometimes lighter, but black where most 
exposed, f The Russian traveller, v. Miklucho-Maclay, became acquainted with people 
named Orang Sakai in his journey through Johore in 1874-75. He stated that 
the hair consisted of very fine curls, arranged in a compact mass projecting for a short 
distance from the head, and formed a good guide to the purity of the race. J He re- 
garded the people as Melanesians, though they approached the Negritos of the Philip- 
pines. The height of the men varied from 1450 to 1650 mm. (4 ft. 7 in. to 5 ft. 4 in.), 
and the heads were mesocephalic to brachycephalic. M. de Quatrefages figured § from 
photographs natives, said to be Sakais from Perak, in one of whom the hair was smooth 
and in two others was frizzled. Mr Abraham Hale has seen the Sakai people in the 
Kintah district of Perak, and has given an account || of many of their customs. He 
states that an ancient race the Semangs are also found in Perak, on the right bank of 
the Perak river, whilst the Sakais inhabit the left bank. 

Hale did not describe the physical characters of the Sakai, but stated that their 
primitive dress consisted of bark cloth twisted round the waist and drawn between the 
thighs. The nasal septum was pierced to wear a porcupine quill or a bone, and the ears 
were often pierced. The women had the hair standing out from the head in a great 
mop ; they wore bracelets, and ornamented the face and breast with red figures. The 
Kelantan Sakais from the north-east were finer-looking men than those in the Kintah 
district. 

At the instigation of Professor Vtrchow, Mr Vaughan Stevens travelled in the eastern 

* After this Memoir was in type I received, through the courtesy of Major Bannerman, M.D., the Madras 
Christian College Magazine for September and October 1900, in which is an article by Mr C. Hayavadawa Rau, B.A., 
on the origin of the Servile Classes and Hill Tribes of South India. In this article Mr Rau discusses, from the 
physical, social, linguistic and intellectual points of view, the Negrito theory of the origin of the Dravidians, and regards 
the theory as untenable. He draws the inference that all the indigenous tribes foimd by the Aryan immigrants in 
Southern India belonged substantially to one and the same Dravidian race. 

t These accounts are abstracted in G. W. Earl's work on the Native Races of the Indian Archipelago, London, 1853. 

I Verh. der Berliner Ges.fiir Anth., etc., 1876 and 1891, p. 837 ; Joum. of Straits Branch of Royal Asiatic Soc, 1878. 
§ Les Pygm&s, Paris, 1887, pp. 54, 55. 

II Journal of Anth. Institute, vol. xv. p. 285, 1886. 



CRANIOLOGY OF PEOPLE OF INDIA. 119 

part of the Malay peninsula. He sent to Berlin specimens of the hair of a tribe which 
he called Blandass or Belendas, a name which he seems to use as synonymous with Sakai.* 
Virchow states that the hair varied in length from 59 to 26 cm. ; it was ebony in 
colour, the more slender examples being paler, and in a child pale reddish brown. In 
no specimen was it curly or spirally twisted, though at the tip it bent into a crescentic 
form. At a later date Stevens forwarded specimens of the hair and a skull from the 
Panghan tribe (Panggan), on the east side of the peninsula. The men cut the hair close 
to the scalp, but left a tuft at the top of the occiput. The tuft was said to be of 
'peppercorn' shape, and only 5 to 10 mm. above the scalp. The hair was black, 
slender and spirally twisted as in the Negrito, and could at once be distinguished 
from the hair of the Belendas tribe. The Semang tribe of Perak on the western side 
have apparently a similar tuft of hair, possessing the same character. Virchow figures 
the skull, which was short, broad and high, kypsibrachycephalic ; the length-breadth 
index being 81 '5, the length-height 76"9. The glabella and supra-orbital ridges were 
prominent. The face was broad and low, chamseprosopic ; the orbital index 80, was 
microseme ; the nose was short, with a low bridge, mesorhine ; the upper jaw was 
strongly prognathic; the cranial capacity was 1370 c.c. 

In 1897 Dr R. Martin undertook a journey through the Malay peninsula with 
the object of seeing the wild tribes in the interior.! He distinguished the appearance 
of the Semangs, who live especially in the north and in part in the Siamese provinces, 
from the Sakais, who are found especially in Perak, Selangor, and the west of Pehang. 
The Semangs, he says, had black skins, black frizzled hair, and were doubtless closely 
allied to the Negritos of the Philippines. In the Sakai the skin of the breast and body 
was reddish brown in tint, whilst on the face it was a medium brown with yellowish 
brown shades ; the hair was black, but with a brownish shimmer in certain lights, and 
throughout was wavy, which distinguished it from the frizzled hair of the Semang, and 
from the stiff hair of all Mongols, including the Malays. The stature of the Sakai men 
averaged about 1500 mm. (4 ft. 9 in.), that of the women 1420 mm. (4 ft. 6 in.). 
The head, from numerous measurements, had a mean length-breadth index 79 ; the 
face was broad, but pointed at the chin, mesoprosopic in its proportions, the nose had 
slight projection, but with broad alae, which were deeper than the septum ; the 
tegumentary part of the lips, especially the upper, was thick. They painted the face 
and breast with red, white and black spots, put hollow cylinders of bamboo into the 
ears and filled them with grasses, which formed a green frame around the face of the 
women. The men bored the nasal septum and passed through it a piece of wood or 
porcupine quill. 

I am indebted to Mr Nelson Annandale, who travelled in 1899 in the northern 
part of the peninsula, for photographs of a Sakai youth aged about 15, who lived in 
the Aring district, a hilly country in Kelantan, in the centre of the peninsula. He had 

* Verh. der Berliner Ges.fiir Anth., etc., November 1891, July and October 1892. 
t Mitteil. der Naturiviss. Ges. in Winterthur, Heft ii., 1900. 



120 PROFESSOR STR W. TURNER ON 

been captured by the Malays as a child, and had been circumcised and brought up as 
a Mahommedan. His skin was dark, approaching black ; the forehead was almost 
vertical, the nose was short, with a low flattened bridge and wide alee, the upper lip 
was thick and prominent, the facial configuration was negroid, but the hair, instead 
of being woolly or frizzled, was straight, and apparently three or four inches 
long. 

In March 1891 I received from my former pupil, the late Dr W. Duncan Scott, an 
imperfect skeleton, which he believed to be that of a Sakai, with a letter giving an 
interesting account of the people. Dr Scott had accompanied his chief, Mr Abraham 
Hale, in his visit to a tribe of Sakais inhabiting the hill-tops above the Kintah river at 
a place called Tanjang Keukong. Dr Scott is the officer referred to by Mr Hale in 
the appendix to his account of these people.* Dr Scott writes as follows : — The Sakais 
occupy the hill country in the Malay peninsula as far south as the north end of Johore. 
The skull and bones were found in a valley watered by the Kampar river, a tributary of 
the Kintah river, about 25 miles from Batu Gajah. The hills are inhabited by scattered 
groups of Sakais. The bones were found on a rude platform, about 6 feet from the 
ground, in a lean-to hut under the shelter of a hill. The hut was made of boughs of 
trees, and the bones were further protected by a sort of cage of branches.! 

The Sakais, he says, were an active, well-proportioned people, with stout muscular 
limbs, and of a sturdier make than the Malays. Their stature was probably on the average 
about 5 feet 2 inches, though some may be 5 feet 3 or 4 inches. The skin was lighter 
in colour than in the Malay, and but little deeper in tint than in the Chinese, though 
rather brown than yellow, and those who lived in the hills were lighter than those who 
occupied the low ground. The features, on the whole, were broad, but not markedly so, 
and the lips were not especially thick. The hair was black, and in those seen by Dr 
Scott was inclined to be long, wavy, reaching to the shoulders ; but in some tribes he 
says that it was stiff, slightly curled, and stood out like a mop around the head, whilst 
in the people who lived more to the south it was in short corkscrew-like curls. The 
eyes, as far as he recollects, were dark brown. The gait was peculiar, with a step and 
swing from the hip. 

The younger women wore the Malay sarong round the waist and over the breasts ; 
the older women were generally content with a sarong or piece of bark cloth or fringe 
of fibrous roots around the waist, and with necklaces of shells, seeds, or monkeys' teeth. 
The men wore a loin-cloth made of bark, and on festive occasions they wound a strip of 
bark round the head. Many of the men ornamented the face with a white patch on the 
cheek, and the girls had the face covered with red and brown streaks. They carried on 
the back a light basket of rattan to hold fruit or small animals taken in the jungle. 
They obtained iron choppers, or parangs, from the Malays, but could not smelt the 

* Journ. Anthrop. Inst., vol. xv. p. 299, 188G. 

t Mr Nelson Annandale has kindly given me photographs which he took of a Sakai rock shelter in Patalung 
which resembles the hut descrihed by Dr Scott. 



CRANIOLOGY OF PEOPLE OF INDIA. 121 

ore. Their weapons were spears of bamboo and the sumpitan with poisoned darts. Dr 
Scott also wrote an account of their religion, houses, dances, etc., but as this closely 
corresponded with the description already in print by Mr Hale, it is unnecessary to 
reproduce it. 

The skull presented to me by Dr Scott is, I think, that of a man. apparently about 
middle life ; the lower jaw is unfortunately absent. 

In the norma verticalis the outline was broadly ovoid, with almost vertical side walls, 
not ridged, but flattened in the sagittal region ; the parietal eminences were not promi- 
nent, and the skull was without the marked disproportion between the breadth of the 
frontal and parietal regions seen in the Andaman crania. The length-breadth index was 
74*6, and the skull was dolichocephalic. The vertical index was 76*5, and the height was 
more than the breadth. The parietal longitudinal arc was much the longest. A shallow, 
vertical-transverse constriction, as if from the pressure of a band during infancy, was 
immediately behind the coronal suture. The parieto-occipital slope passed gradually 
downwards, and the occipital squama was rounded. 

The glabella and supra-orbital ridges were distinct but not excessive, the forehead 
only slightly receded, and the frontal eminences were not prominent. The nasion was 
a little depressed ; the nasal bones were small, concave forwards, and projected feebly at 
the tip. The nasal spine of the superior maxillae was short. The anterior nares were 
wide, and the nasal index, 5 8 '5, was strongly platyrhine. The floor of the nose and the 
incisive region of the jaw were separated by a shallow ridge. The upper jaw was 
orthognathous. The orbital index, 78, was microseme. Although the absence of the 
lower jaw prevented the complete facial index being taken, the short nasio-alveolar 
diameter, as compared with the interzygomatic breadth index, 3 4 '5, gave a low 
chamseprosopic character to the face. The palato-m axillary region was broad in relation 
to the length, and the index was 125. 

The teeth were not much though several had been lost during life, and the 

sockets were absorbed ; their cro were smaller than in the Andaman Islanders. The 
sutural denticulations were short and relatively simple. A small Wormian bone was in 
the left parieto-mastoid suture, and in the left pterion was a large epipteric bone. The 
left jugal process was tuberculated. The mastoids were feeble, and the skull rested 
behind on the posterior border of the foramen magnum. The cranium was phseno- 
zygous. The cranial capacity was microcephalic. 

From the examination of the bones of the skeleton, especially those of the limbs, it 
was evident that the person had been of low stature. The atlas was the only true 
vertebra which reached me. 

Pelvis. — It was small in general dimensions : the alse were not expanded or very 
translucent : the pectineal lines were not knife-like : the prae- auricular sulcus was 
distinct. The sacrum had a feeble anterior concavity : its index, 102, was platyhieric, 
but the length was almost equal to the breadth. The conjugate diameter of the pelvic 
brim was distinctly greater than the transverse, and the brim index, 108 "5, was highly 



122 



PROFESSOR SIR W. TURNER ON 



dolicho-pellic. The highest indices which I had previously recorded # were in a male 
Australian 1 16, a male Bushman 109, and a male Malay 105. The highest brim index in 
the male Andaman pelves which I have measured was 102. The want of expansion in 
the iliac fossae was shown by the small breadth between the crests of these bones. The 
width of the pubic arch, with its angle 80°, gave a feminine aspect to the pelvis which 
led me at first to doubt, notwithstanding the cranial characters, if the skeleton were 
that of a male. Of the numerous pelves which I have measured in the female sex, no 
specimen up to this time has shown the conjugate diameter to exceed the transverse, 
whilst in the males of savage races this is not unfrequent. In the Sakai pelvis the 
conjugate was so much in excess that I regard it as confirmatory evidence of the 
skeleton being of the male sex. I may also state that in a male pelvis in each of the 
following races I have measured the subpubic angle as follows : — Andaman, 78° ; 
Chinese, 76° ; Malay, 76° ; Bush, 72°. 



Measurements of Pelvis. 





mm. 


1. Breadth of pelvis, 

2. Height of pelvis, 












211 
164 


3. Breadth-Height Index, 

4. Between ant. sup. iliac spines, 

5. Between post. sup. iliac spines, 

6. Between ischial tubera, 












77-7 
193 

80 
126 


7. Vertical diameter of obturator foramen, 








38 


8. Transverse diameter of obturator foramen, 








31 


9. Obturator Index, ..... 








81-6 


10. Subpubic angle, 

1 1 . Transverse diameter of brim, 












80° 
106 


12. Conjugate diameter of brim, 

13. Pelvic or Brim Index, 












115 
108-5 


14. Intertuberal diameter, 












107 


15. Depth of pelvic cavity, 

16. Length of sacrum, 












72 
94 


17. Breadth of sacrum, . 












96 


18. Sacral Index, 












102 



Upper Limb. — The Clavicles were slender bones, feebly curved, and with faintly- 
marked grooves for the subclavius muscles. The right bone was 120 mm., the left 123 
mm. long. The Scapulae were small in their dimensions, with well-marked muscular 
impressions indicative of strong muscles ; the axillary border was concave in its 
long diameter, the supra-scapular notch was shallow. The right bone was 122 mm. 
long and 83 broad, its scapular index was 68 ; the left bone was 123 mm. long and 
80 broad, its index was 65. The mean index of the two scapulae was 66'5, which is less 
than the mean of 69*8 obtained by Flower and Gaeson from twenty-one scapulae of 
Andaman Islanders, and of 70'6 by myself from six scapulae of that race. The Humeri 
had strong muscular impressions and distinct musculo-spiral grooves ; no intercondylar 

* Challenger lleport on Human Skeletons, part xlvii., 1886. 



CRANIOLOGY OF PEOPLE OF INDIA. 123 

foramen or supra-condylar process was present. The bones of the forearm, though 
short, were well-proportioned and with distinct muscular impressions, but the styloid 
processes were feeble. 

The dimensions were as follows : — 

Right. Left. 

Humerus, head to trochlea, . 253 mm. 246 mm. 

Eadius to tip of styloid, 



,, base „ 

Ulna to tip of styloid, . 
articular surface, 



203 „ 201 
200 „ 199 
222 

222 



The radio-humeral index was 80 *2, or dolichokerkic,* a proportion which these bones 
have in common with the Andaman Islanders and with the Negritos measured by Meyer 
and Tungel and by Hamy, which expresses that the forearm was in its relation to the 
upper arm proportionately longer than is found in Europeans. 

Lower Limb. — The right femur, tibia, fibula and tarsal bones had been sent to me. 
The Femur, though small, was well-proportioned, and with strong muscular impressions. 
The head showed the slight prolongation of the articular surface on to the upper part of 
the anterior surface of the neck, which I have elsewhere named the extensor area, t The 
upper end of the anterior intertrochanteric line was unusually strong, and indicated 
that the ilio-femoral ligament which takes so important a part in the maintenance of 
the erect attitude had been well developed. The gluteal ridge and the linea aspera were 
strongly marked. The flattening of the upper third of the shaft which I described in 
some aboriginal femora,^ and which Manouvrier has subsequently termed platymery, 
was not present, and there was no external infra-trochanteric ridge distinct from the 
gluteal ridge. The transverse diameter of the upper third of the shaft was 23 mm., the 
antero-posterior 18 mm., and the index of platymery was 78. The transverse diameter 
of the shaft opposite the nutrient foramen was 20 mm., the antero-posterior diameter was 
23 mm., and the pilastric index was 115, which expresses the relatively strong pro- 
jection of the linea aspera. The articular surface of the internal condyl was not 
specially prolonged upwards and backwards. 

The Tibia was well-proportioned. The head was somewhat retroverted ; the internal 
condylar surface was concave, the external was plano-concave. The shaft was not 
platyknemic ; its breadth in the middle was 18 mm., its antero-posterior diameter 
22 mm., and the index was 81*8. At its lower end the tibia had a well-marked 
astragalar articular facet, prolonged to the front of the bone. Associated with this was 
a corresponding prolongation of the upper articular surface on the astragalus, which was 
almost continuous with the anterior convex surface for the scaphoid. So well defined 
was this additional tibio -astragalar articulation that, as Arthur Thomson and Havelock 
Charles have shown, the ankle joint must have been frequently acutely flexed as takes 

* For the use of this term see my CJiallenger Report on Human Skeletons, part xlvii., 1886. 
t Address to section of Anthropology in British Association Reports, Toronto, 1897. 
+ Challenger Report, op. cit., page 97. 

VOL. XL. PART I. (NO. 6). S 



124 PROFESSOR SIR W. TURNER ON 

place in the attitude of squatting.* The Fibula was well marked in its surfaces, borders, 
and muscular impressions. 

The long bones had the following dimensions : — 

Right. 
Femur, maximum length, ....... 368 mm. 



,, oblique length, 
Tibia condylar surface to tip of malleolus, . 
„ „ astragalar surface, 

Fibula, maximum length, 



365 
299 
295 
299 



It will be observed that the tibia and fibula are of the same length. The tibio- 
femoral index, calculated from the oblique length of the femur and the condylo-astragalar 
length of the tibia, was 80"9, and the leg, therefore, scarcely reached dolichoknemic pro- 
portions ; a result similar to that which I obtained from the measurement of four 
skeletons of Andaman Islanders, in which the mean index was 81*2. An index of the 
relative length of the upper and lower limbs, called intermembral index, has been 

,, . -, , , , n ,, £ -, humerus + radius x 100 ,. -, ,, 

obtained by the following formula tt-. , m which the maximum 

lemur + tibia 

length of the bones was taken. In the Sakai skeleton this index was 68 '3, which is some- 
what less than the mean 6 8 '9 obtained some years ago by Flower and myself from the 
measurement of a number of skeletons of Andaman Islanders. In both these people 
this index is relatively low, and points to the bones of the shaft of the upper limb, being 
short in comparison with those of the lower limb. The relative lengths of the humerus 

and femur have been calculated by the formula -. , and the index is 687, a 

lemur 

number which is less than the mean 70 obtained by Flower and myself in the Andaman 

Islanders. 

With the view of obtaining an estimate of the stature of the person whose skeleton 

I had examined, I compared the length of the femur and tibia with that of the 

corresponding bones of a male Andaman islander in the University Museum,! whose 

articulated skeleton was 4 feet 6-^ inches (1385 mm.) in height. The oblique length of 

the femur in this skeleton was 385 mm. (15^ ins.), and the condylo-astragalar length 

of the tibia was 322 mm. (12^ ins.) — together, 707 mm. (27^ ins.) : whilst in the 

Sakai skeleton the corresponding diameters in the two bones were together only 660 

mm. (26 ins.), which points to a stature about two inches less than that of the 

Andaman islander. 

A short time after the receipt of the skeleton of the Sakai, Dr Duncan Scott 

presented me with a skull found in the jungle in Ulu Pahang, on the eastern sea-board 

of the Malay peninsula, immediately to the north of Johore. The collector from 

whom Dr Scott received it could not say whether it was a Sakai or a Malay, but 

* Journal of Anat. and Phys., 1889-1894. 

t I am indebted to Colonel Cadell, V.C, for the gift of this skeleton, which I have had articulated. 



CRANIOLOGY OF PEOPLE OF INDIA. 125 

thought from the locality that it was the former. Although there is a doubt as to 
the race, I have thought well to give a brief description of it. 

The skull had been injured, and there was no lower jaw; it was obviously that of 
a man ; the loss of teeth and the absorption of the sockets gave the impression of an 
aged person, but the cranial sutures were unossified and scarcely denticulated. In the 
right coronal were two sutural bones, in the left pterion a small epipteric, and in the 
lambdoidal suture several small Wormian bones. In the norma verticalis the cranium 
was broadly ovoid, raised along the sagittal line, and sloping rapidly down to the 
parietal eminences, below which the sides were somewhat convex. Its length-breadth 
index was 79*4, a little below the brachycephalic numerical limit, and the vertical 
index was only 76*6, — so that in the proportions of length and breadth to height, it 
had the brachycephalic rather than the dolichocephalic character. The parietal was the 
longest of the longitudinal arcs. The actual length of this skull was 6 mm. more than 
the one just described, but its breadth was 13 mm. greater, which accounted for the 
higher length-breadth index. The parieto-occipital slope was gradual, and not more or 
less abrupt than one sees in the more characteristic brachycephalic crania ; the occipital 
squama did not project much behind the inion. 

The glabella and supra-orbital ridges were feeble ; the frontal eminences were 
scarcely marked ; the forehead receded a little ; the nasion was not depressed ; the 
nasal bones slightly projected, and the bridge was shallow ; the anterior nares were 
wide, but the height of the nose, 51 mm., brought the index into the mesorhine 
group ; the nasal spine of the superior maxillae was feeble. The absorption of the 
incisive alveoli made it impossible to determine the original projection of the jaw, and 
the gnathic index, 94*9, is only approximative. The broken zygomata prevented the 
width of the face from being taken. The cranial capacity was mesocephalic. 

Although much remains to be done to complete our knowledge of the inhabitants 
•of the Malay peninsula, it is obvious that in addition to the Malays, who dwell on the 
sea-coast, and the Siamese invaders in the northern provinces, whose appearance in 
the peninsula is probably of relatively recent date, the hill-districts are peopled by 
tribes who, in their external characters and cranial configuration, differ from each 
other. From the preceding narrative it will be seen, that whilst some tribes named 
Semangs and Panghans have the black skin and frizzly hair characteristic of the 
Negritos, in other tribes the skin is not so dark, and the hair, though black, is not 
frizzly or woolly, but is relatively straight and several inches long. Travellers do 
not always differentiate by descriptive names the straighter-haired from the frizzly- 
haired people, and by some the name Sakai is employed to designate both varieties 
of aborigines who dwell in the hilly and jungly districts. If the frizzly-haired, 
black-skinned Negrito people are the aboriginal inhabitants, those with straighter hair 
doubtless also represent an ancient race. The question, however, naturally arises, 
whether there may not have been in the course of centuries an intermixture and 
cohabitation of the Negrito race with the straight-haired Malays from the sea-board, 



126 PROFESSOR SIR W. TURNER ON 

as well as with the straight-haired Siamese who have entered the peninsula from the 
north, so as to lead to a modification in the physical characteristics of the people and 
the production in certain districts of a mixed race. 

As regards the cranial configuration, the skull of the frizzly-haired Panghan, 
described by Professor Virchow, was brachycephalic ; and the figure which he has 
reproduced obviously represents a type of skull resembling that of the Andaman 
Islanders. The skull form, therefore, confirms the view of the presence of a Negrito 
people in the Malay peninsula. 

Of the two skulls which I have described, the one from the Kintah district, from 
its locality and the nature of the interment, must be regarded as of an aboriginal race 
and not a Malay. The skull was dolichocephalic, a proportion which belongs neither to 
the Negrito nor to the Malay. From Dr Scott's description of the people, to whom he 
gives the general name of " Sakai," it would seem that the hill-tribes in this district 
had long and not frizzly hair, a skin not black but lighter in colour than the Malay, 
which, conjoined with the dolichocephalic skull, gave race characters differing materially 
from the Negritos. These people, however, have, like the Negritos, a low stature. 
The skull from Pahang, on the other hand, differed so materially in its proportions 
and general appearance from the Kintah specimen, that it cannot, I think, have 
belonged to the same tribe or race, — the proportion of the length-breadth index, 
though numerically mesaticephalic, 79*4, was essentially brachycephalic, though the 
parieto-occipital slope was not abruptly steep. In the form of the vertex and the 
proportions of the nose it differed from the Kintah skull, but its injured condition 
did not admit of a complete comparison being made. I hesitate, therefore, to give an 
opinion on the race to which it had belonged. 

From the consideration of the whole question there seems to be little doubt that in 
the hill regions of the Malay peninsula two aboriginal races are met with, distinguished 
from each other by the colour of the skin, the characters of the hair, and the form of 
the cranium, though both possess in common a low stature. 



CRANIOLOGY OF PEOPLE OF INDIA. 127 



EXPLANATION OF PLATES IV.-VII. 

The Plates and Figures are numbered in sequence with those in Part I. of this Memoir. 
For the Photographs from which the figures are reproduced I am indebted to Mr W. E. Carnegie Dickson, B.Sc. 

Fig. 15. Gond, Godavery District, Central India, profile. Table I. 

„ 16. The Same, full face. Table I. 

„ 17. The Same, vertex. Table I. 

„ 18. Kandh, Khoorda, Orissa, profile. Table I. 

„ 19. The Same, full face. Table I. 

„ 20. Bhumij Tribe, Manbhum, $ aet. 30, profile. Table IV. 

„ 21. The Same, full face. Table IV. 

„ 22. The Same, vertex. Table IV. 

„ 23. Tamil-speaking native of Madras, profile. Table II. 

„ 24. The Same, full face. Table II. 

„ 25. Uriya, Baghmari Village, Orissa, profile. Table VI. 

„ 26. The Same, full face. Table VI. 

„ 27. Veddah, metopic skull, male, <J profile. Table IX. 

„ 28. Veddah, Batticaloa, E. Coast of Ceylon, $ full face. Table IX. 

„ 29. Mtinda, Ranchi $, aet. 24, profile. Table III. 

„ 30. Andaman Islander, £ profile. Table X. 

„ 31. The Same, full face. Table X. 

„ 32. The Same, vertex. Table X. 

„ 33. Sakai, Malay peninsula, profile. Table X. 

„ 34. The Same, full face. Table X. 

„ 35. Section through skull of Juang, $, page 128. I.M., No. 443, Table V. 

„ 36. Section through skull of Munda, $ , page 128. I.M., No. 26, Table JII. 



128 



PROFESSOR SIR W. TURNER ON 



The Anteroposterior almost mesial sections show the contour of the crania and the radial 
measurements. 




Fig. 35. — Juang. 

f.m. plane of foramen magnum. 

b. the basion : the lines drawn from which to the points on the circumference are radial from 
that point, and measure in millimetres as follows : — ■ 







Juang. 


Munda 


b.al. 


basi-alveolar radius, 


103 


95 


b.n. 


basi-nasal „ 


106 


101 


b.g. 


basi-glabellar ,, 


111 


111 


b.br. 


basi-bregmatic „ 


142 


128 



b.p. a radial line perpendicular to the 
plane of the foramen magnum, 
b.l. basi-lambdal radius, 
b.oc. basion to occipital point, 



J uang. 

145 

120 
101 



Munda. 

133 

116 
94 




Fig. 36.— Munda. 



CRANIOLOGY OF PEOPLE OF INDIA. 



129= 



CONTENTS OF PARTS I. and II. 



Part I 



Introduction 






Vol. xxxix. 


PAGE 

703 


Hill Tribes 








. 


703 


Kukis 






. 




704 


Luahai Hillmen 








705, 


709 


Chin Hillmen . 








707, 


713 


Tonkal Nagas . 








708, 


717 


Nepal 










724 


Burma 










725 


Karen, Shan 








726, 


737 


Siamese 






. 




739 


Chinese 










741 


Classificatory Value of Brachycephalic 


and 




Dolichocephalic Proportions 




743 


Intermixture and Isolation 




744 


Isolation of Esquimaux 




745 


Isolation of Australians 




746 


Explanation of Plates 










747 



Part II. 

Introduction Vol. xl. 59 

Aborigines 60 

Gond 61 

Oraon 65 

Male" Paharia, Hillmen of Rajmahal ... 66 

Kharwar 67 



PAGE 

Kandh 68 

Nagesar or Kisan ...... 70 

Bhuiya 72 

Korwa 73 

Miinda, Ho, Larkha Kol 74 

Bhiimij 82 

Turi 84 

Juang ........ 85 

Bhima 88 

Koydwar 88 

Bunjana or Bunjara 89 

Kamar and Lobar ...... 89 

Ahir-Goala 90 

Teli 92 

Uriya 92, 107 

Comparison of Aboriginal Crania ... 99 

Kolarians and Dravidians 101 

Dravidians and Australians .... 105 

Veddahs 107 

Veddahs and Dravidians 113 

Negritos 113 

Andaman Islanders . . . . . . 113 

Sakai 118 

Semang 118, 125 

Explanation of Plates 127 

Antero-posterior Sections ..... 128 

Table of Contents 129 



Trans. Roy. Soc. Edinburgh. 

Sir William Turner on "Craniology of People of India." Plate IV. 



Vol. XL. 




Fio. 18.— Kondh. 



Fig. 19.— Kondh. 



Trans. Roy. Soc. Edinburgh. 

Sir William Turner on "Craniology of People of India." — Plate V. 



Vol XL 




Fig. 20.— Bhumij. 




Fig. 22. — Bhurnij. 



ft 





Fig. 21. — Bhumij. 




Fig. 24.— Tamil. 






rt\*. 



rans. Roy. Soc. Edinburgh. 

Sir William Turner on "Craniology of People of India." — Plate VI. 



Vol. XL. 




^ 



Fig. 27.— Veddah. 



Fig. 28.— Veddah. 



fans. Roy. Soc. Edinburgh. 

Sir William Turner on "Craniology of People of India." — Plate VII. 



Vol. XL. 




Fig. 30.— Andaman. 





Fig. 31. — Andaman. 



1 * 

Fig. 32.— Andaman. 






^^F ^r' 




Fig. 33.— Sakai. 



Fig. 34.— Sakai. 



Vffm 



-£RAL*i 




( 131 ) 



VII. — Notes on the Dynamics of Cyclones and Anticyclones. By John Aitken, F.R.S. 

(With a Plate.) 

PART I. 

(Read March 5, 1900.) 

The vertical movements of the earth's atmosphere from which the energy is derived 
which causes the horizontal movements of the air which we call winds, and by means of 
which the moisture evaporated from the surface of land and water is collected and 
carried to the higher regions of the atmosphere, where it is condensed to cloud and 
again distributed in the form of rain over the earth's surface, are of great interest, and 
a thorough knowledge of the laws governing these vertical movements is necessary 
to enable us to arrive at a correct forecast of the coming weather over any area. 

In the present communication I do not intend entering on a review of the work 
which has already been done in this field. Many explanations have been offered of the 
movements of cyclones and anticyclones as a whole, and of the winds within their 
areas, but any detailed reference to these would far exceed the limits of these notes, and 
would, I fear, only complicate matters. In what I have to say there will necessarily 
be much that is old, and I am sorry I must leave to the reader the task of finding out 
what is new, as in a subject of this kind, on which so much has already been written, it 
is impossible to say whether any particular point has not been referred to before by some 
other writer. And further, I shall confine my remarks to what takes place over our 
area and Western Europe, so as to avoid unnecessary verbal complications ; but the 
principles can be easily applied to other areas in the Northern hemisphere, and to the 
reversed direction of circulation in the cyclones and anticyclones in the Southern 
hemisphere. 

At the outset it will be as well for me to make a few elementary remarks on the 
formation of cyclonic movements, as I find that many who take an interest in Meteor- 
ology have rather hazy ideas of how the vortex motion in cyclones is produced. All 
that some seem to think necessary is to have an area of low pressure and that the air 
will rush towards it in spiral paths, just as they see water in a wash-hand basin forming 
a vortex movement whenever the plug is withdrawn and the water allowed to run away. 
Now it must be clearly understood that no vortex will form in air or water that is at 
rest before the low-pressure area is formed ; the air or water under these conditions will 
flow to the low-pressure centre along radial paths and not in spiral ones. The above 
statement requires qualification. When it is said the air or water is at rest it is not 
meant that it is at rest absolutely, which would be an impossibility in this rotating, 
revolving, and space-travelling world of ours. All that is necessary is that the water or 

VOL. XL. PART I. (NO. 7). T 



132 MR JOHN AITKEN ON 

air be at rest relatively to the centre of low pressure — that is, that the centre of low 
pressure and the air surrounding it are all moving in the same direction and at the 
same velocity. Another qualification necessary in the case of the air on the earth's 
surface is, that the area of low pressure be very small, otherwise the different parts of the 
area will have different rates of movement owing to the earth's rotation causing its 
surface and the air near it to move faster near the equator than near the poles, so that 
the air to the south of the low-pressure centre moves more quickly in an easterly direc- 
tion than the air to the north of it — that is, supposing there is no wind. 

Let us now return to the question of the cause of the cyclonic movement. That 
motion relatively to the low-pressure centre is necessary to produce the spiral approach 
of the air or water to the centre is easily illustrated. Take a circular vessel — say 
40 cm. in diameter and 15 cm. deep — filled with water. The vessel should have an 
opening in the centre which can be closed from the outside, so that it can be opened 
without disturbing the water in the vessel. Put some sawdust, or similar substance, in 
the water and mix it with it. Now leave it at rest till all movement in the water 
ceases, then open the outlet in the bottom of the vessel and allow the water to run 
away, when it will be seen that the sawdust suspended in the water moves towards the 
outlet flowing from all directions, and at all depths, in radial lines, without a trace 
of vortex movement. 

Let the conditions be now changed and a slight circular motion be given to the 
water before the outlet is opened. A well-formed cyclone will now be formed by the out- 
flowing water, and the quicker the initial movement the greater will be the number of 
turnings in the spiral path of the water before it arrives at the outlet, and the deeper 
the hollow in the surface of the water over the outlet, while the direction of the spiral 
movement will be the same as the initial movement given to the water. The depression 
of the surface of the water at the centre of the vortex is extremely interesting. If the 
water before the outlet be opened be not perfectly at rest, a faint depression will always 
be detected over the outlet, having in its centre a quickly-rotating vortex of very small 
area. If, however, the initial motion be greater — but it need not be quick — then the 
depression deepens and forms an air-tube extending to the bottom of the vessel, showing 
that the slow initial circular motion has enabled the low-pressure area to generate a 
velocity at the centre of the cyclone sufficient to enable the centrifugal force of 
the water at that part to withstand the hydrostatic pressure at the bottom of the 
vessel. 

On examining these water vortexes there is a point that strikes one as very remark- 
able — namely, the great increase in the velocity of the water as it approaches the centre 
of movement. Not only is the angular velocity greatly increased owing to the shorter 
path required to complete a revolution near the centre, but the absolute velocity is also 
greatly increased. Perhaps this point can be more easily seen by making the experi- 
ment in another form, and using solids in place of liquids. Suspend two balls, A A, 
fig. 1, by long fine wires, either from the same point of suspension, or, to reduce the 



DYNAMICS OF CYCLONES AND ANTICYCLONES. 



133 



complications due to the effects of gravity owing to the balls falling a short distance 

as they approach the centre, suspend the balls from the opposite ends of a short beam 

B, suspended by fine wires, C C, as shown in the figure. The upper ends of the wires are 

fixed to a swivel D, to enable the balls to be put into circular 

movement round their common centre. To each of the balls a 

short cord EE is attached. These cords are passed through a 

small ring F, which is suspended at the level of the balls by the 

wire G fixed to the swivel D. The two cords EE are joined 

below to another swivel H, which has a cord attached to its lower 

end, to allow the balls to rotate round G, whilst the lower cord is 

held in the hand. If we now put the balls into a slow circular 

movement round their common centre, and take hold of the lower 

central cord below the swivel H, note the rate of revolution and 

pull the cord downwards. This will draw the balls towards the 

centre of motion, in the same way as the particles of water are 

drawn into the centre of the vortex. When this is done it will be 

seen that the initial slow motion is rapidly quickened, and that 

when the balls are near the centre they are whirling round each 

other at a great velocity. 

Another way of making this experiment is to remove the 
small ring F and its suspending wire, and tie the balls with a cord 
of about 50 cm. long, then attach to this cord, at a point halfway 
between the balls, a small rod held vertically. If the balls be 
now made to rotate round the rod, and the rod be prevented from 
turning, the balls will gradually wind themselves towards the 
centre, and it will be noticed when making the experiment in this 
way that whilst the angular velocity increases, the absolute 
velocity does not, showing that the mere fact of the balls 
approaching the centre has nothing to do with the increase in the 

velocity observed in the previous experiment. If now, in place of holding the centre 
rod firm, we cause it to rotate on its vertical axis so as to wind the balls towards the 
centre, it will now be seen that the absolute as well as the angular velocity is greatly 
increased, as was seen in the previous experiment, in which the balls were drawn 
together by means of the cords E E. The balls now fly round so quickly the eye can 
hardly follow them. 

Further, it will be noticed that the balls offer a rapidly-increasing resistance to the 
centripetal force. This to a certain extent is to be expected, because as the balls 
approach the centre the centrifugal force increases ; if the velocity is constant it is 
double what it was at first by the time the balls are drawn half way to the centre. 
But on account of the increased velocity which we cannot avoid giving the balls in the 
process, they are enabled to offer still greater resistance to the centripetal force. This, 




Fig. 1. 



134 MR JOHN A1TKEN ON 



which might be called a secondary result, comes in and assists the centrifugal force in 
offering resistance to the change. There are plenty of similar results in physical 
phenomena, where these secondary results assist in resisting the change, as for 
instance, when we compress air. Suppose, as in the above case, we reduce the 
volume to one-half, then we have doubled the pressure, which seems fair enough. 
But the air, with almost human-like dislike to compulsion, heats in the process, and by 
so doing helps to resist the compression till it has had time to cool. These remarks 
may suggest something as to the great power of vortex movements for storing energy. 

The cause of the great increase in the velocity in the balls when they are drawn 
towards the centre is due to work having been done on them. When the balls are 
revolving round their common centre, held by the cord at a fixed distance, no energy 
is communicated to them by the tightened cord, because the force acts at right angles 
to the direction of movement. But when the balls move in a spiral path, then only 
one component of the radial force acts at right angles to the direction of motion, whilst 
another is in the direction of the movement, thus tending to increase its velocity. The 
same explanation applies to the increased velocity of air or water approaching the 
centre of cyclones. 

This resistance offered by the spirally-moving air to be drawn into the centre 
of the cyclone has one important effect. It enables the cyclone to develop more 
energy than if the air moved inwards radially. When the air moves in radially the 
supply is so abundant that a great fall of pressure cannot take place, but when the 
inflow of the air is retarded by the centrifugal force, a greater fall of pressure results, 
and the energy of the cyclone is increased ; and in addition to this we shall see 
later that it adds greatly to the efficiency of cyclones considered as circulating 
engines. 

It may perhaps be as well that I give my reasons for saying that whilst the 
vortex motion gives rise to strong currents— that is, increase of velocity — it yet 
retards the inflow, and by so doing it will allow a lower pressure to be formed in 
the centre. This point can be most easiiy illustrated by means of water vortexes. 
The circular vessel already referred to was used, the outlet being a short pipe 
fixed in the centre of the vessel. In each experiment the vessel was filled with 
water to the same depth, and the time observed that the water took to empty 
when it had no motion before starting to empty — that is, emptied out without vortex 
motion — and when a slight movement was given so as to cause it to form a cyclone 
when emptying. The result was the water took a half longer in the latter case 
than in the former, showing a great retardation due to the cyclonic motion, and this 
retardation results in a lowering of the pressure at the centre, and it also prevents the 
low-pressure area being so rapidly filled up. Care was of course taken in the above 
experiments that the pipe carrying away the water was always full in both cases, so that 
the head of water should be the same in both. This was done by placing a glass disc 
over the outlet and at some distance above it, and making the outlet pipe discharge 



DYNAMICS OF CYCLONES AND ANTICYCLONES. 135 

below water. By these means air was prevented entering either end of the discharge 
pipe. 

For making experiment on the cyclonic movements in air, I have found the 
following piece of apparatus useful. To produce the up-draught a thin metal tube 
15 cm. diameter and fully 2 m. high was used. At the lower end of the tube is 
fixed a circular disc 76 cm. diameter. The disc is supported on three legs, 
15 cm. high, thus leaving an air space of 15 cm. between the disc and the table 
on which it rests. To produce the up-draught three small jets of gas are fitted 
inside the tube near the lower end. To study the circulation produced by the 
apparatus, a number of small light vanes supported on small stands were used, so 
that they could be put to show the direction of the air currents anywhere within the 
area affected. These vanes show the directions of the circulation at the different parts 
of the area affected by the cyclone, but for studying the variations in the circulation 
at different heights from the surface of the table, the fumes from hydrochloric acid 
and ammonia were found to be more useful. These fumes are very suitable for the 
purpose, as they have only a very slight proper motion of their own, rising only 
very slowly, so that their own movements do not interfere much with the cyclonic 
motions. When working with fumes a large plate of glass should be placed below 
the apparatus to give freedom for experimenting, and the fumes are best made by 
placing pieces of paper on the glass and dropping the ammonia and acid on them. 
These papers, being close to the surface, do not give rise to local eddies. 

Before lighting the gas to make an experiment, some fumes should be made 
under the tube, to see if there are any air currents in the room. Suppose there are 
none, and the fumes rise slowly without drifting in any direction, the gas should 
now be lighted and a number of centres of fumes should be started at different 
points under and round the tube, either by dropping the acid and ammonia on 
separate pieces of paper, or by putting them in watch glasses. If we observe the 
fumes under these conditions, it will be seen that they rise and move radially towards 
the hot chimney, moving upwards in even curves, but showing no tendency to rotate 
round the centre. An element is still wanting to produce the cyclonic motion, the 
air must be given some initial movement before the up-draught will take the spiral 
form. Suppose that on first testing the air on the table, we found that it was not free 
from movement, but that there was a slight current blowing across it. If this current 
be equally strong at all points, it will not be of much use in generating cyclonic move- 
ment, but if we put up a screen so as to cut off the current from one side of the area 
and allow it to blow on the other, then we have the conditions necessary for producing 
vortex motion under the chimney. If we examine the fumes rising under these new 
conditions, it will be seen they no longer move radially but are in violent cyclonic 
motion, swirling round and round in the direction given by the tangential current, the 
rising fumes forming graceful ascending spirals. So strong is the circular motion that 
at times the gas in the chimney is heard flaring as in a strong wind. 



136 MR JOHN AITKEN ON 

If there is no cyclonic motion formed when the gas is lit, any light objects lying 
on the table are not disturbed by the radially moving air, but if a good cyclonic 
circulation is set up, then any light bodies, such as sawdust, paper, or tufts of cotton 
wool, which happen to be lying under the chimney, are seen to be lifted up and tossed 
about, generally getting thrown out of the centre of the cyclone by their centrifugal 
force, but the cotton wool is frequently drawn up the centre and discharged at the 
top of the tube. Should there be no current in the room suitable for producing the 
tangential motion, then the cyclone may be formed by blowing by artificial means 
across one side of the area, or over two or more sides if in correct directions. 

Let us now study more closely the movements of the air under the draught tube. 
Suppose we have it arranged so that a gentle current is blowing across one half of 

the cyclonic area, and the air is forming a cyclone under 
the tube, we shall now place the small vanes — already 
referred to — within the area of the cyclone, to show the 
directions of the movements of the air — that is, the winds 
at the different parts of the cyclone. The result is roughly 
shown in fig. 2. The air current over the table is supposed 
to be blowing in the direction of the arrow at the side, and 
to be strongest on that side of the area, and the cyclonic 
movement is roughly indicated by the arrows in the 
diagram. It is impossible to get these directions satis- 
factorily indicated by the vanes, owing to the difficulty of 
Fig. 2. keeping the cross current constant, and the amount of 

curving of the spirally-moving air is constantly changing 
with every change in this tangential component. The arrows, however, show that on 
the side where the tangential current is strongest the in-draught is most tangential,, 
whilst on the opposite side the incoming air moves more radially, or, to put it more 
generally, the air in the right-hand front of cyclones in our area moves more tangentially 
than the opposite left-hand rear position. It should be noticed here that these remarks 
apply to the case where the centre of the cyclone is fixed. Some modification will be 
necessary when applying them to cyclones in which the centre of low pressure is in 
motion. 

We may learn something further with this apparatus if we use fumes to study 
the movements of the air over the different sections of the cyclonic area. One very 
marked result which will be observed is that the air — as shown by the fumes — near 
the surface of the table at all parts of the area moves much more radially than the air 
higher up, and also that the air lying on the surface of the table is drawn into the very 
core of the cyclone, up which it rises in a rapidly-circling path of small diameter, whilst 
the air higher up comes towards the centre along a rising wider spiral path, and forms 
the outer lining of the cyclonic tube. The lower air keeps near the surface till it arrives 
near the centre of the cyclone and then rises, making many more revolutions than the 




DYNAMICS OF CYCLONES AND ANTICYCLONES. 137 

outer air for the same amount of ascent, as roughly indicated in fig. 3. This in- 
draught of the lower air into the core of the cyclone is one of great importance in 
connection with meteorological phenomena, and will be referred to later on. The 
reason for the lower air being drawn into the core is very 
obvious. The air near the ground, or surface of the table 
■in this case, has less tangential movement than the air higher < 

up, owing to its motion being retarded by friction. The ,.-- — ^ 
result of this is that whilst the greater centrifugal force of \ „ 

the upper air keeps it back against the low pressure in the 

cyclone, the lower air as it moves nearly radially offers but 

little resistance to the in-draught. Hence the lowest stratum of air being at the lower 

end of the cyclonic tube, it is drawn into the very centre. 

Anyone can make similar experiments to these without a special draught tube, and 
study for themselves the conditions necessary for the formation of cyclonic circulation. 
All that is necessary is a good fire, with a free-going chimney, and a wet cloth. The 
cloth is hung up in front of the fire and pretty near it, so as to cause a liberal amount 
of condensed steam to rise from its surface. Probably without some arrangement of 
the draughts in the room no cyclone will be formed, and the vapour will rise vertically, 
keeping close to the wet cloth. But if the room has a door or a window in the wall 
at right angles to the fireplace, and at the side nearest the fireplace, so as to cause 
the air coming from it to make a cross current past the fire, then a cyclone will be 
formed and the steam on the wet cloth will be seen circling round, and when the 
cyclone is well formed, all the steam is collected into the centre of the cyclone and 
forms a white pillar extending from the cloth to the chimney. If the cross-draught 
be equally strong at top and bottom of the wet cloth, it will be necessary to screen 
the current from either the top or bottom of the cyclonic area. Should there be no 
suitable draught in the room, then an artificial one may be made in any direction 
-across one side of the wet area. 

We have seen from these experiments that no cyclone can form without some 
tangential movement in the air entering the area of low pressure. The next question 
one naturally asks is — Has this tangential motion any other effect on the cyclone? 
From the fact that some of the air entering the cyclone has motion in a particular 
direction, we would naturally expect that unless an equal amount of air, moving in 
the opposite direction, also entered at the same time on the other side, that the whole 
system would move in the direction of the greatest tangential force. If we examine 
the cyclone produced in our artificial conditions with the draught tube we shall find 
that this is the case. The lower end of the cyclone bends away from under the 
centre of the apparatus, moving in the direction of the tangential current. 

This point can, however, be better illustrated by means of water vortexes. Using 
the circular vessel as before, and in order to make the tangential current on one side 
stronger than on the other, all that is necessary is either to put the outlet for the 




138 MR JOHN AITKEN ON 

water excentric to the walls of the vessel, or more easily by taking a strip of thin 
metal, having a breadth the same as the depth of the vessel and of a length of a little 
more than the diameter, and bend it into its place in the circular vessel, as shown in 

fig. 4. When the water now runs out it all passes round the 

vessel, and as the passage between the outlet, that is the 

centre of the cyclone, and the temporary division is narrower 

than at any other place, the water has to pass this part at a 

much greater velocity than at any other place, and the result 

is, the top of the vortex no longer remains over the outlet, 

but travels in the direction of the quickest moving water, 

showing that, as might be expected, the quickest moving 

water tends to carry the centre of the vortex along with it< 

See fig. 4, where the small dotted circle represents the outlet 

FlG _ 4> and the full circle the top of the vortex, which is carried by 

the water to the right, the direction of movement of the 

water being shown by the arrows. In addition to moving in the direction of the 

strongest current, the centre seems also to be attracted towards the quickly-moving 

area, but to this point I shall not further refer at present. 

Turning now from these experimental observations, let us see how far they help us 
to understand the phenomena in cylones and anticyclones in our atmosphere. At the 
outset I may say that in forecasting attention seems to have been given too exclusively 
to what takes place in cyclonic areas, and too little to the part played by anti- 
cyclones. We have been looking too much on the cyclone as the active member of 
this dual partnership. But I think we will have to admit that the anticyclone is not 
the sleeping partner it is generally supposed to be, whose only duty is to follow and fill 
up the depressions made by the active partner. A closer examination of the part played 
by the anticyclone will show that it also is an active though silent partner in the firm, 
and that it initiates and keeps up its own circulation, and collects and forwards the 
material with which the more showy partner, the cyclone, makes its display. The 
anticyclone also in a great measure directs the path of the cyclone and adds much 
to its cyclonic motion. In fact the vertical circulation seems to be kept up by the 
partners in this dual system playing into each other's hands, and neither could work 
efficiently without the other. 

Let us now look at what the effect would be if there were no cyclones or anti- 
cyclones in our atmosphere. Suppose a large area, say, some hundreds of miles in 
diameter, on the earth's surface over which the air was still, suppose further that the 
sky was cloudless and a summer's sun was shining. After a time the conditions 
would become unstable and columns of air would begin to ascend at many points all 
over the area wherever the air happened to be most highly heated and charged with 
vapour. The result of this would be a disorderly mob of ascending currents without 
leader, organization, or combined effort. These small isolated attempts at vertical 



DYNAMICS OF CYCLONES AND ANTICYCLONES. 139 

movements could never give rise to anything like a systematized and law-abiding 
circulation, though they might result in local disturbances such as thunderstorms 
and rain. 

Let us now suppose the conditions are changed and that an anticyclone is 
blowing at one side of our supposed hot area, and note the change. When the upper 
air descends to the earth's surface, it spreads out in all directions, and if the earth had 
no motion of rotation the air would spread in radial paths from the centre — that is, 
supposing the descending column of air had no motion of its own, which is very 
unlikely. But as little is known on this subject, we must at present neglect it, and 
may safely do so, as probably even if it has motion it will not greatly affect the 
result. Suppose that the descending air arrives at the surface of the earth and spreads 
outwards in all directions, then, owing to the earth's rotation, the air in place of 
moving radially from the centre, goes in spiral paths. This is owing to the air that 
moves in a northerly direction blowing over a part of the earth that has a slower 
easterly motion than the descending air which has come from the south, and the wind 
seems over the northern part of the anticyclone to blow more or less from the west. 
On the other hand, the air moving southwards of the centre flows over an area going 
more quickly eastwards than the descending air, and the wind over that part of the 
anticyclone seems to blow more or less from an easterly direction, whilst the air moving 
east and west from the centre would appear only to have its velocity altered, were it 
not for other causes which come into play, and make the circulation from the anticyclone 
to be, in a general way, spiral all round the centre. As the air to the north of the 
centre moves eastward, and that to the south westwards, the circulation in the anti- 
cyclone is right-handed — that is, in the direction of the hands of a watch with its 
face upwards. 

One effect of spiral circulation, to which we have already referred in the experi- 
mental part of the paper, is that the air near the surface of the ground where its 
motion is retarded by friction moves more radially than the upper air. This causes 
the higher air currents to cross the lower at a greater or less angle, and has the effect 
of checking the rising of the lower air even when lighter than the upper. In our 
atmosphere the case is more complicated than in the experiments, owing to the 
earth's rotation. Over certain areas of the anticyclone the upper and lower airs may 
be moving in nearly the same direction : this will be the case when the upper air is 
moving in nearly the same direction as the surface of the earth at the place. But 
even when the direction of the upper and lower airs is the same, the difference in 
velocity of the two has some influence in checking the lower air from rising. 

Let us now see what the effect of such an organized circulation is in our 
atmosphere. Let the sketch fig. 5 represent an imaginary anticyclone, which we 
have shown circular, though the shape is generally far from being so regular. If 
such a system be established over our imaginary area of sun-heated air, then it will 
be seen that the anticyclonic winds will prevent the formation of local cyclones, and 

VOL. XL. PART I. (NO. 7). TJ 



140 



MR JOHN AITKEN ON 



drive all the moist hot air to its circumference, keeping it near the ground. Suppose, 
now, that the hot air begins to form a cyclone at the outside of the anticyclone, as 
shown in fig. 6, it will be evident it has a supply of hot air collected for it by the 
anticyclone. But not only has the anticyclone collected the material for making 
the cyclone, but it also supplies the cyclone with the tangential force necessary for 
producing the spiral circulation so well known in cyclones. 

The explanation generally given of the spiral movement in cyclones is, that the 
air drawn in from the south has a greater amount of eastward motion than the centre 
of the cyclone, whilst the air from the north has less, and that these oppositely moving 
airs from the two directions cause the whole system to circulate round the centre. 
This, no doubt, is one cause of the circular movement in cyclones, but it is far from 



^"-^N 






/ ^ 




Fig. 5. 



Fig. 6. 



being the only one. This tangential action — due to the earth's rotation — only comes 
into play after the air has travelled a considerable distance towards the centre, whereas 
the air from the anticyclone already has a considerable tangential movement over the 
area between the cyclone and the anticyclone. The true explanation would rather 
appear to be that the cyclone and the anticyclone form one system ; the anticyclone 
forces its air tangentially into the cyclone, whilst the cj^clone draws air tangentially 
from the anticyclone. The earth's rotation is the original source of the rotatory 
movements, and starts the machine, but both intensify the initial motion ; they are, so 
to speak, geared into each other and kept in motion by the earth's rotation, but both 
capable, when conditions are favourable, of developing energy on their own account and 
increasing their rate of rotation. 

We saw in the experimental part that a cyclone in the conditions represented in 
fig. 6 — that is, with strong winds blowing tangentially on one side — cannot remain in 
the same place, but must move in the direction of the strongest winds. It would be 
fatal for a cyclone to remain long in one place ; it would soon use up all the supplies, 
and when all the hot moist air had been drawn in, it would be starved and get weaker, 



DYNAMICS OF CYCLONES AND ANTICYCLONES. 141 

and the depression soon get filled up. So the cyclone has to move on for fresh supplies, 
and if our experimental illustration is correct, it will move along in the direction of 
the strongest tangential winds. 

Now, if we look at the Synoptic Charts issued by the Meteorological Office, we 
shall see that they support this explanation, that these tangential winds are the 
principal cause of the movement of the cyclone as a whole, that the centre of depression 
moves in the direction and nearly parallel to these winds ; or, in other words, the 
cyclone moves nearly parallel with the isobars at the side on which the barometric 
gradient is steepest. Further observation will show that the greater the difference 
in the barometric gradients on the two sides, the quicker is the advance of the cyclone, 
due to the tangential energy on the steep side being greater than on the other. The 
examination of these charts will also show that, whenever the isobars surrounding the 
cyclone become equally spaced on all sides, that is, when the barometric gradient is the 
same all round the centre — or even on the front and sides — that the cyclone travels 
very slowly and is generally in a dying condition. The air under these conditions comes 
to the cyclone with equal velocities from all directions, and there is no tendency for 
the centre to move. The tangential force is still in great abundance, the winds blowing 
in from all directions systematically all round, but there is no unbalanced tangential 
force, and the centre remains over the same area, and as the hot moist air — the source 
of the energy — is soon used up, the winds tend to fall and the depression to fill up. 
This seems to be the history of many of the cyclones with circular and concentrically 
placed isobars, though in winter they seem occasionally to linger for a time, their winds 
then seem to depend a good deal on the energy of surrounding anticyclones. It also 
seems possible that the movements of such cyclones may be determined a good deal 
by differences of temperature over the anticyclonic areas. 

In illustration of these points we shall now refer to some actual examples taken 
from the Synoptic Charts issued weekly by the Meteorological Office, London. These 
charts show the distribution of pressure and direction of winds over Europe from 
observations taken at 8 a.m. and 6 p.m., the day interval being thus 10 hours, 
whilst the night one is 14 hours. There are charts also giving the temperatures at 
8 a.m. Plate I. is a reproduction of four of these charts, showing the distribution 
of pressure over our area during the passage of two cyclones, — the one a typical 
quickly-moving one, and the other a slowly-progressing one. In the charts for 10th 
December 1898 we have the characteristic distribution of pressure, as shown by the 
isobars, for a quickly-moving cyclone; whilst the charts for 9th December 1897 
show the form of isobars associated with slowly-moving ones. In the 1898 cyclone 
it will be observed that the barometric gradient to the south of the centre of the 
cyclone was very steep in the 8 a.m. chart, as shown by the closeness of the isobars on 
that side, whilst the gradients on the other side and in front were easy. The strong 
winds, as the form of the isobars would lead us to expect, are all to the south of the 
centre, and are blowing from the west, and the result was that the centre of this cyclone, 



142 



MR JOHN ATTKEN ON 



which was over the Shetland Isles at 8 a. in., travelled to the east coast of Sweden by 
6 p.m., a distance of 700 miles. During the following night the centre moved in an 
E.N.E. direction at a considerable velocity, but at a slower rate than during the day, 
as the barometric gradients at 6 p.m. would lead us to expect. 

Turn now to the chart for the 9th December 1897. Here it will be seen that 
the barometric gradients are nearly equal all round, and strong winds are blowing 
in all directions systematically round the centre. Now note the slow rate of progress. 
This cyclone appeared on the N.W. of Scotland on the evening of the 8th December. 
Next morning at 8 o'clock it was in the place shown in the chart, having travelled 
a distance of 175 miles in the 14 hours. When this cyclone first appeared the 
barometric gradient was steeper to the south than on any other side. This, no doubt, 
was the cause of the advance of 170 miles during the night. It will, however, be seen 
from the 6 p.m. chart, that the centre moved very little during the day, somewhere 
about 75 miles, and the whole of the following night it was still over the same place, 
having apparently become stationary, as it was still there on the morning of the 10th, 
but the gradients were getting easier, the depression getting filled up. These two 
cyclones were selected — out of many having similar histories — to illustrate the 
point under discussion, and they were selected because they travelled over exactly 
the same track, and at the same time of the year, so that we should only have the 
question of the conditions shown by the shape of isobars to consider. 

To illustrate this point still further, the following table gives in brief the histories 
of a few of the cyclones during the last two years. The table shows the date and 
hour when the cyclone first appeared on the chart. Then there is given the situation 
of the centre of the cyclone, followed by the character of the isobars or distribution 
of gradient, and, lastly, the distance travelled in miles. 



1898. 



Date. 


Hour. 


Position of centre of Cyclone 


Isobars. 


Miles. 


Mar. 1 

2 

„ 3 

„ 4 


8 a.m. 
6 p.m. 
8 a.m. 
6 p.m. 
8 a.m. 
6 p.m. 
8 a.m. 


North-east of Scotland, .... 

North Sea, 

,, • . . . , 
Denmark, ..... 

S. Baltic, ..'.'. 

N. Germany, ..... 




Not much difference. 

>> >j 
„ filling up. 

)> >) 
>> )> 


150 
150 
200 
60 
130 
130 


Oct. 16 
„ 17 
„ 18 
„ 19 


8 a.m. 
6 p.m. 
8 a.m. 
6 p.m. 
8 a.m. 
6 p.m. 
8 a.m. 
6 p.m. 


Off entrance to English Channel. 
>> )> 

>> )> 
West of London, .... 
Midland counties, .... 
Border of Wales, .... 

N. Wales, 




Nearly equal. 
)> >> 
>) )> 

filling up. 

>> !> 

)> » 
» )) 


100 
90 
50 

200 
90 
50 
75 



DYNAMICS OF CYCLONES AND ANTICYCLONES. 



143 



1898. 



Date. 


Hour. 


Position of centre of Cyclone. 


Isobars. 


Miles. 


Nov. 23 
„ 24 
„ 25 
„ 26 


8 a.m. 
6 p.m. 
8 a.m. 
6 p.m. 
8 a.m. 
6 p.m. 
8 a.m. 


Over Ireland, ...... 

St George's Channel, ..... 

Entrance to English Channel, 

)> jj ■ • • ■ 

Over Cornwall, ...... 

Off Land's End, 

Off Cape Finisterre, ..... 


Nearly equal all round. 

>' >) 
)> >> 

!) )) 


190 
150 
75 
40 
120 
110 


Dec. 2 
„ 3 


8 a.m. 
6 p.m. 
8 p.m. 
6 p.m. 


South of Norway, ...... 

North of Christiania, ..... 

East coast of Sweden, . . . 

Over Finland, ...... 


Steep to south. 
>) 


230 
350 
500 


Jan. 12 
„ 13 


8 a.m. 
6 p.m. 
8 a.m. 
6 p.m. 


1899. 

Off north-west of Ireland, .... 
Off north-east of England, .... 
Over south of Gothland, .... 
Over Baltic provinces, ..... 


Steep to south. 
>> 
)> 
>> 


450 
600 
400 


Mar. 28 
„ 29 


6 p.m. 
8 a.m. 
6 p.m. 


Off west coast of Scotland, .... 
Off west coast of Norway, .... 
Over Norway and Sweden, .... 


Steep to south. 


600 
400 


April 6 

„ 7 

„ 8 

» 9 


6 p.m. 
8 a.m. 
6 p.m. 
8 a.m. 
6 p.m. 
8 a.m. 


Off north-west of Ireland, .... 

Over north of England, ..... 

Over south of North Sea, .... 

East of Schleswig, ...... 

Over Holstein, ...... 

South of Denmark, . ... 


Steepest to south. 
Steepest to south-west. 

,, to south. 
Nearly equal all round. 


375 

200 

200 

70 

120 


April 9 

„ 10 

„ 11 
„ 12 


6 p.m. 
8 a.m. 
6 p.m. 
8 a.m. 
6 p.m. 
8 a.m. 
6 p.m. 


North-west of Ireland, ..... 

Off east coast of England, .... 

East of Holstein, ...... 

East of Denmark, . . ... 

South of Sweden, ...... 

Over Stockholm, . . ... 

South of Gulf of Bothnia, .... 


Steep to south. 

Becoming equal all round, 
o >) 

j) >> 
>j i) 


430 
250 
220 
200 
100 
100 


Aug. 16 

„ 17 

„ 18 
„ 19 


6 p.m. 
8 a.m. 
6 p.m. 
8 a.m. 
6 p.m. 
8 a.m. 


Off north of Scotland, 

Over the Skager Back, 

Over south of Sweden, 

Over the north of Baltic, .... 
Entrance to Gulf of Finland, .... 


Steep to south. 

>> 
Becoming equal all round. 

>) >> 

>5 )) 
» )) 


420 

300 

125 

60 

20 



144 



MR JOHN AITKEN ON 



1899. 



Date. 


Hour. 


Oct. 23 


6 p.m. 


,, 24 


8 a.m. 




6 p.m. 


„ 25 


8 a.m. 




6 p.m. 


„ 26 


S a.m. 




6 p.m. 



Position of centre of Cyclone. 



West of Norway, . 
Over Norway and Sweden, 
Over entrance of Gulf of Finland, 
South of Gulf of Finland, 
West of Moscow, . 



Isobars. 



Steep to south-west. 
Becoming equal all round. 



Miles. 



400 
400 
150 
300 
50 
50 



The history of all these cyclones bears out the conclusion that, when the 
barometric gradient is steep on one side, the cyclone travels quickly and nearly 
parallel with the isobars on the steep side, and that, as the gradients become equal 
all round the centre, the advance becomes slow. 

Dr Buchan, in his Introductory Text-Book of Meteorology, points out that the 
isobars in cyclones are frequently elliptical. Now that is just the form we would 
expect them to take when the barometric gradient was steep on one side only 
— that is, with strong winds blowing in one direction. The centrifugal force of these 
strong winds will tend to draw out the front of the cyclone, and make the length 
of the ellipse to point in the direction in which the centre of the storm is moving. 
When the winds are equally strong on all sides there is little tendency for the 
isobars to depart from the circular form, which an examination of the Synoptic 
Charts will show to be the case. 

There is another effect of the inertia of the winds blowing along the steepest 
gradient which will be observed in these charts. Whilst the air from the anticyclone 
on the side next the cyclone is drawn into the cyclonic vortex, the air nearer the 
centre of the anticyclone passes on in the general anticyclonic circulation, and this 
quickly-moving air in the anticyclonic area seems to force back the high pressure in 
front. The effect is to aid the advance of the cyclone by lowering the pressure in front 
of it. This effect will be seen in the chart for the 10th December 1898 (Plate I.). On 
the morning of the 9th the shape of the isobars was similar to that shown in the chart 
for the 10th, but the furthest north point of the 29 '9 isobar, instead of being near the 
eastern limit of our area, was a little to the north of Scotland, and it was driven 
eastwards to the position shown on the morning of the 10th. The curve of this isobar 
kept much the same form as it travelled eastwards. 

We showed in the experimental part that the air currents at different elevations 
coming to the centre of the cyclone move in different paths, the air near the ground 
moving more radially than the air higher up, and it may be asked — Is there anything 
corresponding to this in the cyclones in the atmosphere ? To get an answer to this 
question, the air currents in a number of cyclones have been examined. The position 
of the centre of the depression was taken from the Synoptic Charts, and the air 



DYNAMICS OF CYCLONES AND ANTICYCLONES. 145 

currents were taken from the observations made by Messrs Bolam & Kedpath at Leith, 
along with those made by myself. The direction of the lower current is given by the 
winds, whilst the direction of the upper current is shown by the cloud movement. The 
result of this examination of the cyclones in the atmosphere shows this feature 
in quite a distinct manner. In all cases in which there was any difference in the 
recorded directions of the upper and lower currents, the lower current flowed more 
directly towards the centre of the depression than the upper. It was also noticed 
that the upper current was frequently almost quite tangential, apparently not 
pointing at all to the centre of the depression. The observations used in investi- 
gating this point were almost all taken on the side of the depression on which the 
barometric gradient was steepest and winds strongest, and it would seem to indicate 
that the inflow towards the centre on this side — particularly of the upper air — is 
less than on the other sides. This result is indicated in the experimental part of the 
paper, where it is shown that the air on the side of the cyclone which receives the 
greatest tangential force curves inwards less than the air on the other sides. 

The upper currents moving more tangentially than the lower ones has the effect, 
when a depression is passing any station, of making the upper currents appear to veer 
in advance of the lower. For instance, with a depression to the north of the point of 
observation, the wind will be south of west, whilst the cloud carry will be about west, 
and when the depression has passed eastwards the wind will change to west, whilst the 
carry will have some north in it. It may be as well to note here that it is possible 
that the upper part of the cyclonic column may travel in advance of the lower, owing 
to the friction on the earth's surface acting as a drag on the lower end. If this be 
the case it will in part explain the veering of the upper currents in advance of the 
lower. 

We shall now turn our attention to anticyclones, and see what part they play in 
the vertical circulation of our atmosphere, as too little attention has, I think, been 
given to them. The sun's heat seems always to have been looked upon as the great 
source of the energy in our winds, to the exclusion of the effects of cold. It is as if, in 
studying a steam-engine, we had devoted our attention to the boiler and furnace, and 
neglected the condenser. The engine would no doubt work without the condenser, 
though not so efficiently, but it may be doubted whether heat alone would work a 
cyclone without the cold-driven anticyclone. Its absence, at least, would be a greater 
loss to the vertical circulation than the loss of the condenser to the engine ; unless, 
indeed, the engine was working at a very low pressure. 

It is well known that the mean pressure over continental areas is high during 
winter and low during summer. That is just as the sun's rays during summer, by 
heating the air over continental areas, gives rise to cyclonic conditions ; so the earth's 
radiation during winter gives rise to anticyclonic conditions, and this cooling of the air 
seems to be as true a cause of vertical circulation as the heating of it, though perhaps 
not to the same extent. If this be the case, then we ought to give more attention to 



146 MR JOHN A1TKEN ON 

the anticyclone than we have been giving, as a study of the area under its influence 
will probably assist in forecasting the movements of the cyclone and the weather 
conditions generally. 

An examination of the weather charts for the winter months over our area shows 
that when the temperature is low over any part of it, particularly over the Spanish 
Peninsula and over the north-east of Europe, that as the temperature falls the 
pressure rises — that is, whenever the temperature falls below the mean, an anticyclone 
forms over the cold area, increasing in pressure as the cold strengthens. And, on the 
other hand, when the temperature begins to rise the pressure falls. It must be 
admitted that there are difficulties in studying this subject, as there is not at present 
sufficient information to enable us thoroughly to study the point. We would require 
a complete record of the clouds over the area, so as to enable us to judge how far the 
earth's radiation initiates the change. But I think it may be accepted that, as a rule, 
any extreme cold over our area is generally accompanied by a small amount of cloud, 
and that the cold is due to radiation. An examination of the weather charts shows 
that, on some occasions, when the directive force of the cyclone was small, a rise of 
temperature in the anticyclonic area, by weakening the high pressure, caused the cyclone 
to move towards it. On the other hand, a decrease in temperature in the anticyclone 
may force the cyclone back. These charts also show that, if the temperature over both 
the Spanish Peninsula and the north-east of Europe falls very low at the same time, 
then the whole of Europe comes under anticyclonic conditions, the cyclones being 
driven from our area. 

Let us now turn to the general question of cyclonic circulation, and see if what 
has been stated helps us to understand some of the other phenomena associated with 
cvclones and anticyclones. We have seen that the upper winds, circling from the 
anticyclones and to the cyclones, by moving more quickly, and by moving at an 
angle across the lower air, tends to prevent the latter rising, even though it be the 
lighter. The effect of this, as already pointed out, is to drive the hot moist air lying 
near the earth's surface to the circumference of the anticyclone, where it is picked up 
by the cyclone, and as the spirally moving cyclonic winds also tend to prevent the 
lower air rising, the hot, moist air is swept into the front of the low-pressure area, 
and the upper winds here cross the lower at a considerable angle, the hot moist air is 
compelled to keep near the ground, and, further, the air near the ground having a 
less tangential force, it is drawn into the centre of the depression, where it is drawn 
up, and as we saw in the experiments, forms the core of the cyclone. By this method 
of arranging the air in layers, the cyclone gets the best efficiency out of its material, 
the pressure falling from the circumference to the centre, whilst the temperature 
rises towards the centre of low pressure. 

The effect of cyclonic circulation in keeping the hot moist air near the ground 
explains why the air in front of a cyclone is always hotter and moister than the 
air in the rear. The lower air sent forward by the anticyclone is swept off its 



DYNAMICS OF CYCLONES AND ANTICYCLONES. 147 

circumference by the cyclone and drawn into the cyclone curving round the front of 
it, and in its passage it gets added to it all the hot moist air in front of the cyclonic 
area. After the cyclone is past it is evident that, as it has drawn up the surface air 
over the area of its track, that what was previously the higher, drier, and purer air 
will have taken its place ; hence the coolness, freshness, and purity of the air after the 
disturbance has passed. The cyclone has brought down to us the air we would have 
got if, before it passed, we had ascended a considerable distance from the earth's surface. 

The above seems to give a fair explanation of the presence of the hot moist 
air in front of cyclones. Still, some may feel inclined to say that is not the whole 
explanation, and that there is something else in the air over that area which gives 
it a peculiar heavy feel — something, in fact, to which no hygroscope is sensitive. To 
explain these peculiar sensations produced by this air, there is a point to which 
reference might be made. It is one which I do not think has ever been investigated 
or even referred to, and it is one which may help to explain the peculiar physiological 
effects experienced under these conditions. In front of a cyclone where the pressure 
is falling there will be a considerable amount of air rising from the soil and rocks 
underneath the surface. This air will come charged with moisture, and more or less 
changed in its composition by contact with the soil ; it will also bring with it any 
impure gases there may be in the soil. That such air does rise there can be no 
doubt. If we observe the surface of the ground while the barometer is falling, 
after a slight fall of snow which has come before the frost, so that the temperature of 
the ground is not below the freezing point, we shall see little bare spots where the 
snow has melted. As these little patches are scattered all over bare ground, gravel 
walks, etc., where the subsoil is uniform, they can hardly be due to heat conducted 
upwards, but rather seem to be the result of hot air rising from the ground. The fact 
that the ground under these bare patches is more porous than elsewhere also points 
to the rising air as the cause of the melting. Though moist air rises from under 
the soil with a falling barometer, yet it is difficult to get any satisfactory way of 
measuring its amount. We can easily find out the air space in any sample of 
soil, and a few tests have been made in this direction. In place of taking the air 
capacity, the unoccupied space was measured by means of water. A cylindrical 
vessel that held 17 litres of water was used. In making the tests this vessel was 
filled with the soil, firmly tramping in layer by layer ; water was then added till 
it showed on the top. In making this measurement it is necessary to fill the vessel 
with water from below, otherwise it will not penetrate all through the soil. In the 
tests this was done by thrusting a small pipe down through the centre of the soil, and 
pouring in the water at the top of the pipe. Well-packed garden soil, tested in 
winter, when it was wet, gave the following result. In one case 3 litres of water 
were required to fill up the air spaces, and in another it required 3*4 litres, so that 
something between i to ^ of garden soil is air space. A clay soil would probably 
have less air space. When sand was treated in the same way, it required a little 

VOL. XL. PART I. (NO. 7). X 



148 MR JOHN AITKEN ON 

over 5 litres in one case and a little under 5 in another, which shows that about 
^ of sand is air space. The garden soil in the test vessel would probably be as 
closely packed as the soil in the garden, but the sand would not be so firm as it was in 
its undisturbed condition, as I found it possible, by continued shaking while in 
the water, to make it more compact, and bring fully \ a litre of water to the 
surface. 

These figures seem to indicate that about \ of cultivated soil is air space, and 
about \ is air space in consolidated sand. With these figures it would be easy to 
calculate the amount of air that each cubic foot would send to the surface with 
a given fall of the barometer. But this will not help us much, as it is difficult to 
get the air space in the lower undisturbed strata and find the mean depth from 
which the air rises. From the porosity of many soils it is evident that a consider- 
able amount of air must ascend and descend with every change of pressure, and 
this air will have properties different from the air in the general circulation, and 
may give rise to certain physiological effects. 



PART II. 

(Read May 7, 1900.) 

In the experiments described in the first part of this paper, the cyclonic move- 
ments were produced under very artificial conditions, the centre of low pressure 
being kept in a fixed position and the ascending column of air protected by solid 
walls. It seemed, however, that if the views set forth in Part I. were correct, that 
there was no reason why these experimental illustrations might not be extended, 
and made without much apparatus, and in free air, so as to allow us to study the 
motion of the centre of the depression as well as the spiral movements of the air 
towards it. On trial I found this could be easily done, and soon had the pleasure of 
seeing small cyclones forming and travelling across the experimental area, and the 
spirally inflowing air was seen moving towards the onward moving centre of low 
pressure. 

The apparatus required for these experiments is very simple, and consists of a 
small platform, the surface of which can be heated for supplying the hot air required 
to make the cyclones. On this hot surface a wet piece of cloth or paper may be 
laid, or fumes may be formed, as in the previous experiments, to enable the eye 
to follow the movements of the air. Over this heated area, under certain conditions, 
cyclones are seen to form and travel across its surface. To enable the experimental 
surface to be heated, it was made in the form of a shallow tin box, closed on all 
sides and provided with two small pipes, one for the entrance of steam to heat it, 
and another for draining away the condensed water. This box is 75 cm. square 



DYNAMICS OF CYCLONES AND ANTICYCLONES. 149 

and 1 cm. deep. This heated platform is placed on a table, and the boiler for 
producing steam to heat it at some distance away, so as to prevent the heat of the 
boiler producing disturbing currents near the experimental area. 

When we watch this hot area we will see the steam rising from its wet surface, 
and according to the draughts in the room, or absence of them, it will either rise up 
in an irregular manner, or be drifted across the hot area to the one side, but showing 
in neither case any tendency to form cyclonic movements. Suppose the air in the 
room to be perfectly still and the hot air ascending vertically. If we now blow gently 
over one side of the hot area, a cyclone at once forms which collects the hot air into 
its core and carries it to a considerable height. This cyclone soon dies away if we 
cease to supply the tangential energy. 

Let us now see what the effect is if there is a draught across the hot area, and 
we alter the conditions by placing a screen across the current so as to shield one 
side of the hot area whilst it is allowed to blow over the other. A cyclone will now 
at once be formed at a short distance from the edge of the screen — a sort of eddy, in 
fact. It does not, however, remain in its place, but at once begins to travel across the 
hot area, in the same direction as the cross air current, rotating in the direction 
given by this tangential current, and rising to a considerable height above the 
platform. 

It is not necessary that the screen protecting the one side of the platform 
should have a vertical edge, though such an edge is best suited for making eddies. 
The edge of the screen may be shaped like a magnified comb, 
as shown in fig. 7. When so shaped the screen exerts very 
little effect on the current at the tips of the teeth, but more 
near their base, thus allowing a stronger current to blow over 
one side of the area than over the other. If this screen be put 
up across the current a cyclone will at once be seen forming 
near the points, and so soon as formed it begins to travel away 
across the hot area in the direction of the strongest tangential 

air current. Before this cyclone has gone far another forms near the screen, and it 
in turn passes, following the course of the first, and so on, cyclone following cyclone 
so long as there is a cross current and a heated area. 

It may be as well to point out here that though there may be a slight tendency 
for eddies to form at the edge of the screen, in the above experiment, yet this 
tendency is very slight and has but little to do with the formation of the cyclones. 
If we repeat the experiment, without heating the experimental area, and using fumes 
to show the movements of the air, it will be found that only very slight eddying 
effects can be detected. Any that are formed with a screen having a vertical edge are 
small, irregular and broken, and frequently cannot be traced at all, and when the comb- 
like obstruction is used no eddying effect is produced unless there is an ascending 
column of air. The question of the necessity of any eddying effect of the screen in 




150 MR JOHN A1TKEN ON 

starting the cyclonic movement in these experiments is disposed of by the experiment 
previously described, in which it is shown that cyclones are formed in still air when a 
horizontal current is made by blowing across one side of the ascending column, and 
without the intervention of a screen. The screen in these experiments is only used as 
a convenient method of protecting one side of the hot area from the horizontal current. 
If we wish to be more realistic we may crush up a piece of paper roughly into the 
form of a mountain ridge and put it in the place of the screen, with the result that 
cyclones go on forming as before. 

When the air from the natural draught in the room flows over the hot area at the 
same velocity at all parts, the rising steam does not ascend far, but keeps close to the 
hot surface, and is irregular in its movements. But when a cyclone is formed, most of 
the steam is collected into a rapidly whirling vertical column, which ascends to a 
considerable height — to a metre or more above the hot surface, and often presenting the 
appearance of a well-defined column, as it rises through the clearer air. 

In making these experimental cyclones, it was noticed there must be a definite 
relation between the amount of heating and the velocity of the cross current. If the 
heating be slight the cross current must be slow, otherwise the cyclonic movement 
will not be properly formed owing to the weakness of the ascent, before it is swept 
off the experimental area ; whilst with hotter air a stronger current may be permitted, 
with the result that a more violent cyclonic movement is produced, which penetrates 
the upper air to a greater height. 

The use of steam in these experiments is evidently open to many objections, 
other than the great amount of heat required to evaporate the water. Although it is 
water that plays a part in these experimental cyclones as well as in those in nature, 
yet in the two cases the part played by the water is reversed. In nature the water 
goes up as vapour, and when it condenses it liberates a great amount of heat, which 
prevents the temperature of the air falling so much as it would if no condensation 
took place, so aiding in the ascent of the column. But in the experimental cyclones 
this action is reversed, much of the water goes up in the cloudy or condensed form, 
and as in its ascent it gets mixed with more air, the water particles get evaporated 
and heat is absorbed. So that whilst the water taken up as vapour in the cyclones in 
nature increases the energy of the motion, it checks the movements in the artificial 
ones. Condensed water vapour or what we often call steam is thus not the best thing 
to use for showing these cyclonic movements, but it has the advantage that it is pro- 
duced all over the experimental area, so that we can by means of it see the beginning 
and trace the movements of the cyclones. Fumes of hydrochloric acid and ammonia 
may be used, but in that case it is necessary to cover the experimental area with a 
sheet of glass, which is almost certain to crack with the heat. If the glass plate is 
not used the acid and ammonia may be put in watch glasses. Working with fumes 
we get a much greater violence of movement and greater ascent, owing to the air 
being more highly heated, but as the liquids evaporate very rapidly they require 



DYNAMICS OF CYCLONES AND ANTICYCLONES. 151 

frequent renewal, and the rising fumes are patchy, thus allowing the core of the 
cyclone to be often invisible, and they do not often show a well-defined core of 
fumes. 

These experiments are sometimes difficult to repeat with any degree of certainty, 
so much depends on the cross currents that happen to be in the room, which vary with 
changes in the outside temperature, winds, etc., and inside heating. For this reason it 
has been found advantageous to use some method of making a cross current that would 
be completely under control. An ordinary screw-shaped fan of 75 cm. diameter does 
very well for the purpose. Owing to a fan of this construction not delivering its air in 
a uniform horizontal flow, but with an irregular somewhat spiral motion, it was placed 
at a distance of about 1^ metres from the hot area, and into the space between the 
fan and the hot area was fitted a horizontal surface, so as to cause the air to acquire a 
horizontal flow before arriving at the hot area. With this apparatus no difficulty has 
been experienced in repeating the experiments. 

These miniature cyclones illustrate many of the points referred to in the first 
part of this paper. The slower rise of the air over the hot area when the circulation 
is uniform across it, that is, so to speak, anticyclonic, and the collecting together of 
the lower hot air, and the drawing of it up by the cyclone, and the power of the 
whirling column to penetrate the higher regions, is well shown. These small cyclones 
also illustrate the dependence of the spiral movements on the tangential current both 
for their velocity as well as direction of rotation. They also illustrate that the direction 
and the rate at which the cyclone as a whole travels is dependent on the direction and 
velocity of this tangential current. 

If the cyclones be watched for a time whilst the draught in the room is not 
constant in direction or force, it will be seen that the stronger the tangential current 
the quicker the centre of depression moves along with it, and the more rapid is the 
rate of rotation, and if the draught slows down and reverses, then the direction of 
the movement of the centre of the cyclone also reverses, and it goes back on its track. 
Further, if there is no tangential force, as when there are no draughts across the area, 
then no cyclone is formed, and if formed during a temporary cross current it will die 
away and cease to rotate when the cross current ceases. Again, cross currents of equal 
force on opposite sides of hot areas keep the cyclone in one place and rapidly rotating. 

It is not necessary to make special apparatus for making these experimental 
cyclones, as it will be found that a simple arrangement first tried is sufficient for the 
purpose. It consisted of a large sheet of tin plate ; a thick sheet of iron would have 
been better. This w r as covered with two or three sheets of thick paper well soaked in 
water. This is placed over a stove or other means of heating it sufficiently to cause 
steam to rise freely from its surface. When steaming freely the wet surface is removed 
to a table, to be away from the draughts rising from the stove, and one side of the 
hot surface is protected from cross draughts by means of a screen. When this is 
done the cyclones will be seen travelling over the steaming surface. 



152 MR JOHN AITKEN ON 

It seems probable that the small cyclones often seen in nature are produced under 
similar conditions to those above described. These small natural cyclones are often 
seen on dusty roads whilst the sun is shining, the whirling column having a core of 
dusty air, and the centre of motion travelling along the road, tossing up the dust and 
other light objects as it moves along. On one occasion 1 had the opportunity of 
seeing one of these small cyclones in a large park in early spring. The wind, which' 
was very light, was cold and from the north, but the sun was very hot. The move- 
ments of the cyclone were easily seen as it tossed up the dry leaves in its path, 
whirling them up to a height of four or five feet and scattering them all round. The 
path of the cyclone was due south — that is, in the direction of the wind — the distance 
travelled being more than a hundred yards. As there were a number of large trees in 
the park, it was easy to see that the necessary conditions were present for starting and 
carrying on the cyclonic movement. It seems probable that these small cyclones are 
of more frequent occurrence than we are aware of, but owing to the absence of light 
bodies — such as dust, leaves, etc. — there is nothing to indicate their presence. 



[Additional Note. Received February 19, and read March 4, 1901.] 

If both the direction of revolution and the direction of movement of cylones as a 
whole are determined by the anticyclones, it may be asked — Why do cyclones over our 
area almost always move in an easterly or north-easterly direction, and so seldom in 
other directions ? and why do these north-easterly moving cyclones generally travel 
so much quicker than those moving in other directions ? The reason for so many 
cyclones moving in a north-easterly direction would appear to be due to there being 
generally a high-pressure area to the south of us, and accompanied with this, there is 
generally hot moist air coming from the Atlantic and blowing to the north of the high- 
pressure area, and the cyclones form in this hot moist air and travel in the direction of 
the winds blowing out of the anticyclone lying to the south. That is, the frequency of 
these north-easterly moving cyclones is due to the conditions being more generally 
favourable for the formation of cyclones on the north-west side of the anticyclones, 
than on any of the other sides. 

Turning now to the question of why these easterly moving cyclones should travel, 
as a rule, so much more quickly than those moving in other directions. It has been 
pointed out that the cyclone is formed in the low-pressure area between two anti- 
cyclones, and that it moves in the direction in which it receives the strongest 
tangential current. If a cyclone were situated between two equally strong anticyclones, 
it would receive equally strong winds on opposite sides, and it would not move, as it 
would receive equal amounts of air from both anticyclones, and as these equal amounts 



DYNAMICS OF CYCLONES AND ANTICYCLONES. 153 

of air would have equal and opposite velocities, there would be no tendency for the 
centre of the cyclone to travel. But a little consideration will show us that the air to 
the north-western side of anticyclones, in our area, will generally have a greater velocity 
than the air on any of the other sides. The high-pressure areas which regulate the 
movements of cyclones over our area are situated to the south-west of Spain, and over 
Siberia and northern Asia. Now, the air descending from high elevations over these 
areas has, in all probability, come from the upper general air circulation, and was 
previously moving from the equator towards the north pole. It will therefore have a 
greater easterly rate of motion than the surface of the earth where it descends, on 
account of it coming from a lower latitude, and further, it will also have a northerly 
motion. The result of this is, that the air descending from the upper parts of the 
atmosphere, while it tends to move spirally outwards all round over the high-pressure 
area, yet owing to it having a northerly motion and a greater easterly motion than the 
surface of the earth where it descends, the air moving to the northwards and eastwards 
will have a much greater velocity relatively to the earth than the air which moves south- 
wards and westwards. Further, over Europe the high-pressure area to the north is 
always much weaker than the one to the south, and is sometimes absent, so that the 
cyclone is always more influenced by the anticyclone to the south than the one to the 
north, and it thus receives its north-easterly motion from the strong winds on the north- 
west side of the southern anticyclone. These remarks only explain in detail how cyclones 
are affected by the general easterly drift of the atmosphere over our area. 

An examination of the weather charts, however, shows that if a cyclone receives its 
strongest winds from any side of an anticyclone, it will move in the direction of these 
winds. If, for instance, it receives its strongest indraught from an easterly direction 
on the south side of the anticyclone, it will move to the west, or it may move 
northwards along the west side of the anticyclone, or southwards along its east side, 
but as the winds on these sides are generally feeble, the cyclonic movements are 
generally slow. 

There is another point to which reference should be made here, as it has lately 
assumed considerable importance. For long it was held that cyclones were due to a 
a low-pressure area being formed by a rising column of hot moist air towards which the 
surrounding air flowed in spirally ; while lately it has been contended that cyclones are 
only secondary effects due to the interaction of air currents, and are, in fact, eddies in 
the atmosphere formed by the general circulation of the earth's atmosphere. These 
two theories thus attribute the energy of cyclones to two different causes. According to 
the first theory the cyclone receives its energy from the hot and moist air; whilst 
according to the other it gets its energy from the general air circulation. The one 
theory we might call the convectional theory, the other the dynamical or driven 
theory. The question then comes to be, which of these two theories seems to be the 
most probable. To many it may seem difficult to imagine how the dynamical theory 
ever originated. The diameter of cyclones is so very great it is difficult to imagine any 



154 MR JOHN AITKEN ON 

way in which the air currents in the atmosphere could produce eddies hundreds of miles 
in diameter. 

Are there not, however, differences in these two forms of cyclonic movement by 
means of which we can distinguish the one from the other, and say whether the cyclones 
in our atmosphere are convectionally or dynamically driven ? I think there are. One 
way in which we may distinguish between the two kinds is in the direction of the 
circulation. In a convectionally driven cyclone the circulation is spirally inwards, 
whereas in a dynamically driven one we would expect it to be spirally outwards. In 
a dynamically driven cyclone in our atmosphere we would be entitled to expect an 
inward current near the surface of the earth, owing to the velocity there being retarded 
by friction ; the walls of the cyclone would therefore be weak at that part, and air would 
be drawn in at the surface of the ground, and it would also probably be drawn in at the 
top. Now, is there any evidence of a general outward circulation in cyclones with in- 
draught at top and bottom ? 

For information on this point we cannot do better than turn to the valuable and 
very important results obtained by observations on clouds made by means of the 
nephoscope and theodolite, and published in the Report of the International Cloud 
Observations, prepared under the direction of Willis L. Moore, Chief of the Weather 
Bureau, by Frank H. Begelow, M.A., and published last year by the Weather Bureau, 
Washington, U.S.A. If we turn to the series of diagrams in the above Report 
showing the direction and velocity of the circulation in cyclones, we shall see that at only 
one cloud level does the circulation show any tendency to be outwards. The following 
is a summary of the results taken from the Report, pp. 435-6 : " Beginning with the sur- 
face, it is seen (1) that all the vectors have an inward component up to the cumulus, the 
inner increasing in strength ; (2) that they continue inward in the levels from the strato- 
cumulus to the cirro-cumulus, except that there is a slight tendency to turn outwards on 
the exterior circle, the alto-stratus again showing average conformity with the others ; 
(3) the tendency is still inward in the cirro-stratus and cirrus level in the interior, but 
apparently lawless over the outer parts." From the above it will be seen that at all 
levels except the strato-cumulus the circulation is inwards. This tendency to outward 
circulation at the one level is evidently due to the cyclone having at the strato-cumulus 
level its greatest rate of rotation, as shown by the diagrams, and this high velocity 
of rotation at this level would appear to be due to the air in the anticyclone also 
having its maximum velocity at the same level. Though the evidence here shows the 
direction of almost the whole of the circulation to be towards the centre, and thus 
points to the circulation being convectionally driven, yet as there may be some hesitation 
in accepting this evidence as final on the point, as all the circulation is not inwards to 
the top, I shall therefore now proceed to point out another and more definite way in 
which we can distinguish between dynamically and convectionally driven cyclones. 

In a convectionally driven cyclone the velocity of movement of the air, both absolute 
and angular, increases from the outside towards the centre, whereas in a dynamically 



DYNAMICS OF CYCLONES and ANTICYCLONES. L55 

driven one the reverse is the case, the air in I lie outer parts moving quicker than the air 
m the inner. Judged by this teat the evidence is entirely in favour of the theory that 
cydoaes aire oonveotionally driven. An examination of the diagrams in the Report <>/ 
the International Cloud Observations above referred to show in a marked way that 
in cyclones the velocity of the wind increases towards the centre. These charts do 
mil show any great increase of velocity towards the centre <>f the winds at the surface 
of the earth, but they show thai as we ascend to greater elevations the increased 
velocity becomes mora marked, and is very great at the strato-cumulus level, and up 
through tin- cirro cumulus, alto cumulus, alto-stratus, and into the cirro-cumulus level, 
;i result we would not expect to find if cyclones were dynamically driven. 

There is another point in connection with the source of energy in cyclones to which 
reference may be made here, and which seems to support, the above conclusion. It 
ojolones are convectionally driven we would expect them to lend to form and move 
over areas where the air is relatively hot, or moist, or both. II' we examine Dr 
Buohan's maps of the isobars and winds of the world, and his corresponding maps of 
the isotherms, and also Dunwoody's maps of the storm tracks of the world, all in 
Bartholomew's Physical Alius, Vol. III., we will find this supposition receives con- 
siderable support. Confining our attention to the area over Europe and the eastern side, 

Of the Atlantic, it will be seen thai in winter the general air circulation over this area, is 
from the south west, blowing OUt of the high-pressure area, situated at this season to 

the south-west of Spain. It, is this warm south-westerly wind that carries the high 

temperature at this season northwards to Iceland and Scandinavia, and gives rise to the 
lipcurving over this area, of the isothermal lines shown in the maps, and this hot moist 

air, driven northwards between the cold air on both sides, would seem to be the cause 

and SOUTOe of energy of the. cyclones which tra.verse this area, during the. winter months. 
The maps of the storm tracks show that the storms coming towards our area, from 
the western Atlantic move generally along one track till they pass Newfoundland, 
where the track divides ill two, and the storms travel over one of the two routes. 
A number of them go north-eastwards over Scandinavia, whilst the others move across 
England and eastwards over the Continent. Confining our attention tO the more 
northerly route, it will lie seen from the maps that, during winter this track is at its 
furthest north position. In summer the conditions become somewhat, changed, the 

general circulation does not blow so much from the south, the winds being at this 

on ahout west-south-westerly, and the isol hernial lines no longer curve, northwards 
to the extent, they did iii winter, and the track of the storms is now situated at its 
furthest south position, the relatively hot and moist air being now more to the south 
than it was in winter. From this it will he seen thai, the track of the cyclones over 
our area moves northwards as the isothermal lines curve northwards with the approach 
of winter, and again coming southwards when the isotherms lend to 1 1 a, ve an east and 
westerly direction, the storm track thus keeping over the relatively hot, and moist area,. 

VOL. XL. PART I. (NO. 7). Y 



156 MR JOHN AITKEN ON DYNAMICS OF CYCLONES AND ANTICYCLONES. 

The movements of the southern storm track seem to be governed by the same law. 
In winter it attains its most south erly position, drawn southwards apparently by the 
hot moist air of the Mediterranean, over which area the storms move at this season, 
but when summer comes the continental area to the north becomes warmer than the 
Mediterranean, and the track of the storms moves northwards, and in summer is across 
continental Europe. It will be noticed that these two storm tracks move in opposite 
directions at the same season, the northern track moving south in summer and north in 
winter, while the southern one moves north in summer and south in winter. 

It thus appears that storms tend to form and move over areas in which there is a 
supply of hot moist air, and to change their tracks so as always to follow the changes 
in the position of the best supply, and it is difficult to understand why this should be 
so, unless the hot moist air is the cause and source of energy in the cyclone. 

Another consideration which leads us to suppose that convection currents play an 
important part in cyclones is the greater violence of the winds over cyclonic than 
anticyclonic areas, a result we would not expect to find unless some source of energy 
came into action in the cyclonic area. All these considerations point to the conclusion 
that however important the action of anticyclones may be in the formation of cyclones, 
yet cyclones are, to a very large extent, convectionally driven. 

The general circulation over our area, as pointed out, is more from the south during 
winter than during the summer months. This change is partly brought about by the 
weakening during the latter season of the anticyclone to the south-west of Europe, but 
Apparently much more to the disappearance of the anticyclone over Siberia and 
Northern Asia. In winter, Eastern Europe and Northern Asia are covered by a large 
-and well-marked high-pressure area, and it would appear that it is this high-pressure 
area to the north-east which causes the anticyclonic circulation to turn more to the 
northwards in winter than in summer, so that the high winter air temperature and hot 
Gulf Stream water which carry the high winter temperature to Iceland and Scandinavia 
would appear to be greatly due to the high-pressure area over Siberia and Northern 
Asia. I fear I must apologise for adding one more theory to the many explaining the 
high winter temperature of the north-west of Europe. It seems strange that the cold 
over the northern parts of Europe and Asia should play any part in the abnormally 
high winter temperature of the sea and the lands surrounding the north-western parts 
of the Atlantic. 



c. Edin. 



Vol. XL. 



Mr. Aitken on the Dynamics of Cyclones. 

ARRANGEMENT OF ISOBARS IN QUICK MOVING CYCLONES. 



10th DECEMBER 189 8. 



8 A.M. 



6 P.M. 





ARRANGEMENT OF ISOBARS IN SLOW MOVING CYCLONES. 




t.tUTCHIX &30N.EDIN* 



( 157 ) 



VIII. — Observations of the Edinburgh Rock Thermometers. By Thomas Heath, B.A. , 
Assistant Astronomer, Royal Observatory, Edinburgh. (With Four Plates.) 

(Read February 18, 1901.) 

The New Rock Thermometers. 

The accompanying Tables I. and II. contain the readings from May 1888 to December 
1899 of the new set of deep rock thermometers erected in June 1879 at the Calton 
Hill Observatory, to replace the old set which were destroyed in September 1876. The 
tables are in continuation of, and are similarly arranged to, those published by the 
Royal Society of Edinburgh in Vol. XXXV. part 3 of the Transactions, along with 
a paper by the late Prof. Piazzi Smyth. The tables published with Prof. Smyth's 
paper contain the observations made between October 1879 and April 1888, being the 
beginning of the series with the new set of thermometers. 

The construction, testing, and placing in position of these thermometers have already 
been described at length in a previous paper by Prof. Smyth, published in Vol. XXIX. 
part 2 of the Transactions. It is unnecessary therefore to do more than recapitulate 
here the principal facts concerned in the mounting of the instruments. The contract 
for the construction of the thermometers was given to Messrs Adie & Sons, Opticians, 
Edinburgh, and the actual work was carried out by their foreman, the late Mr Thomas 
Wedderburn, under the immediate superintendence of Mr R. Adie. The thermometers, 
when originally placed in the bore-hole in the rock of the Calton Hill, were arranged as 
follows, counting from the surface of the rock to the centres of their respective bulbs : — 



t v at a 


depth 


of 250 inches. 


^2' " 


M 


125 „ 


^3' >> 


»J 


50 „ 


^4> ); 


?? 


25 „ 



There was also a similarly constructed thermometer placed with its bulb an inch under- 
ground, and an air thermometer was hung inside the box with its bulb a few inches 
above the surface. All, except the air thermometer, had 30 inches of tube, of wider 
calibre than the rest of the stem, attached to their upper ends above the surface, for 
scale readings. In their construction care was taken to make the tubes and bulbs in 
all particulars similar to the old thermometers, broken pieces of which had been retained 
for patterns. The stems are, however, shorter than the old ones. After each thermometer 
had been put in place, fine sand was poured into the hole in sufficient quantity to receive 
the next shorter thermometer, till the whole set was in place. In the case of the old 
set the mouth of the hole was closed with plaster of Paris, or some such material. This 
VOL. XL. PART I. (NO. 8). Z 



158 



MR THOMAS HEATH ON 



plan was not adopted with the new set, as it was thought possible that the hard material 
had something to do with the unaccountable fracture in 1861 of the second longest of 
the old set. After the new thermometers had been some time in position, it was noticed 
that the sand was gradually settling down, and that the shorter thermometers were 
slowly sinking. In 1880, as measured by Prof. Piazzi Smyth, their bulbs were then 
below the surface of the rock, 

^ 250 inches, t 2 127*5 inches, t 3 57*0 inches, and t A 34"5 inches. 
In May 1889 they were again measured by Prof. Copeland, and found to be below 

the surface, 

t 1 25 If inches, t 2 130-| inches, t s 58^ inches, t i 35^f inches. 

In August 1900 their positions were once more measured, and they appeared to 
have sunk still further, their bulbs being then below the surface, 

t x 251| inches, t 2 133| inches, t s 60J inches, t 4 37J inches. 

Altogether from the date of their establishment in the rock up to last year, the 
thermometers have sunk, 

t-y If inch, t. 2 8 \ inches, t 3 10^ inches, t± 12£ inches. 

Whether anything can be done, without risk to the safety of the instruments, to 
replace them in their original position or to prevent them sinking further into the 
bore-hole, is a question which will have to be taken into consideration at an early date. 

Plate I. gives a graphic representation of the rise and fall of temperature of the 
four thermometers, as shown by the annual means taken quarterly. These are compared 
with the shaded air temperature curve and the rainfall in Scotland, and with the sun- 
spot curve. The last-named curve has been plotted from the sunspot numbers accord- 
ing to the late P. Wolf, and A. Wolfer. It is remarkable that the series of maximum 
temperatures shown for 1882 correspond to a period in the sunspot cycle which is further 
removed from the sunspot minimum than has ever occurred with this series of observa- 
tions, including those of both the old and new thermometers. Another remarkable 
feature is a dip in the curve at 1898. which goes through all the thermometers, affecting 
even t 1 to a slight extent. It is no doubt connected with the rise in the sunspot curve 
in the same year. The air temperature and rainfall curves have been laid down from 
the table printed on page 186, the numbers used being the quadruple annual means for 
quarterly periods. The sunspot curve has been plotted from the following table : — 



SUN-SPOT NUMBERS ACCORDING TO R. WOLF AND A. WOLFER. 



1877, . 


. Ill 


1883, . 


. 65-3 


1889, . 


. 6-3 


1895, . 


64-0 


1878, . 


. 3-8 


1884, . 


. 633 


1890, . 


. 71 


1896, . 


41-8 


1879, . 


. 77 


1885, . 


. 49-9 


1891, . 


. 35-6 


1897, . 


262 


1880, . 


. 31-5 


1886, . 


. 26-1 


1892, . 


. 730 


1898, . 


26-7 


1881, . 


. 54-4 


1887, . 


. 13-5 


1893, . 


. 84-9 


1899, . 


12-1 


1882, . 


. 58-1 


1 888, . 


. 67 


1894, . 


. 78-0 







OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 



159 



Table I. — The Edinburgh Royal Observatory Rock Thermometers. 

Original Reading. 



Date. 


t 


l 


t 


i 


t 




t 


t 


h 


Air. 


















Surface 






Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Theorem. 


Each 




Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Each 
Reading. 


Reading. 


1888. 






















May 7 


45-25 




42-49 




41-80 




42-55 




49-6 


55-6 


14 

21 


45-16 
45-10 


45-14 


42-66 
42-92 


42-82 


43-00 
43-98 


43-54 


44-45 
46-23 


45-13 


44-5 
507 


46-2 
56-8 


28 . 


45-04 




43-22 




45-39 




47-30 




45-0 


46-3 


June 4 


44-99 




43-64 




45-61 




46-00 




42-8 


45-0 


11 
18 


44-98 
44*98 


44-98 


44-00 
44-25 


44-11 


45 -48 
46-48 


46-21 


46-79 

48-37 


47-54 


49-7 
52-2 


55-4 
55-4 


25 


44-98 




44-54 




47 29 




49-00 




49-2 


50-3 


July 2 


45-00 




44-89 




48-08 




49-76 




51-6 


53-7 


9 


45-05 




45-27 




48-28 




49-39 




53-0 


57-2 


16 . . . 


45-09 


45-10 


45-59 


45-57 


48-52 


48-80 


50-31 


! 50-34 


50-5 


49-8 


23 


4514 




45-90 




49-31 




51-38 


1 


54-4 


57-6 


30 


45-22 




46-21 




49-80 




50-88 




49-5 


51-2 


Aug. 6 


45-31 




46-54 




49-62 




50-56 




50-9 


54-4 


13 
20 


45-40 
45-50 


45-45 


46-78 
46-99 


46-87 


49-98 
49-96 


49 94 


51-40 
50-71 


51-12 


54-1 
52-4 


57-5 
54 


27 . 


45-60 




47-18 




50-20 




51-80 




53-9 


56-5 


Sept. 3 


45-71 




47-36 




50-18 




50-97 




52-8 


55-1 


10 

17 


45-80 
45-92 


45-86 


47-50 
47-64 


47-55 


50-08 
49-77 


49-92 


50-30 
50-40 


50-39 


48-0 
51-4 


49-9 
56-0 


24 


46-01 




47-70 




49-63 




49-90 




49-1 


49-9 


Oct. 1 


46-08 




47-72 




49-09 




48-61 




41-8 


42-0 


8 


46-19 




47-73 




47-63 




45-58 




44-4 


48-8 


15 . 


46-27 


46-26 


47-60 


47-55 


47-20 


47-68 


46-19 


47-13 


46-3 


51-0 


22 


46-34 




47-41 




47-08 




4677 




44-1 


43-0 


29 


46-42 




47"29 




47-40 




48-51 




48-9 


50-0 


Nov. 5 


46-45 




47-21 




47-32 




46-33 




42-9 


43-3 


12 
19 


46-48 
46-54 


46-50 


47-16 
47-04 


47-06 


46-25 
45-91 


46-22 


44-65 
44-80 


45-16 


42-2 
46-4 


44-5 
• 50-5 


26 


46-55 




46-84 




45-40 




44-85 




40-6 


38-3 


Dec. 3 


46-60 




46-68 




44-60 




42-95 




47-1 


52-6 


10 


46-59 




46-44 




45-10 




44-40 




39-5 


39-3 


17 . 


46-58 


46-58 


46-30 


46-28 


44-18 


44-16 


42-40 


42-65 


40-6 


42-2 


24 


46-58 




46-09 




43-80 




42-90 




41-9 


42-6 


31 


46-55 




45-87 




43-10 




40-60 




360 


39-0 


1889. 






















Jan. 7 


46-52 




45-64 




42-30 




40-60 




35-3 


32-3 


14 
21 


46-49 
46-46 


46-47 


45-35 
45-09 


45-23 


42-00 
41-80 


42-02 


40-10 
40-80 


40-62 


36-8 
39 7 


37-9 
41-9 


28 


46-40 




44-85 




42-00 




41-00 




40-2 


43-9 


Feb. 4 


46-34 




44-66 




42 20 




40-80 




35-5 


35-7 


11 

18 


46-25 
46-23 


46-24 


44-53 
44-35 


44-41 


41-30 
40-40 


41-20 


38 80 
39-00 


39-52 


30-8 
44-8 


30-7 
50-0 


25 


46-14 




44-09 




40-90 




39-50 




35-7 


35-6 


Mar. 4 


46-06 




43-90 




40-20 




37-90 




31-6 


31-5 


11 

18 


46-00 
45-92 


45-96 


43-70 
43-45 


43-59 


39-70 
40-30 


40-20 


38-00 
40-10 


39-08 


35-2 
38-9 


37-3 
38-3 


25 


45-85 




43-30 




40-60 




40-30 




45-4 

| 


47-0 



160 



MR THOMAS HEATH ON 



Table I. — continued. 



Date. 


t 


L 


t 


i 


t 


) 


t 


4 


h 


Air. 


















Surface 






Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Theorem. 


Each 




Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Each 
Reading. 


Reading. 


1889. 






















April 1 . . . 


45-77 




43-24 




41-30 




41-60 




42 2 


45-5 


8 


45-66 




43"23 




41-30 




40-40 




38-5 


39-5 


15 


45-58 


45-59 


43-24 


43-23 


41-10 


41-62 


40-20 


41-61 


39-5 


42-5 


22 


45-51 




43-20 




42-00 




42-95 




43-3 


45-7 


2S . . . 


45-44 




43 25 




42-40 




42-90 




43-7 


47-3 


May 6 . . . 


45-38 




43 35 




43-15 




44-41 




45-5 


46-8 


13 

20 


45-32 
45-29 


45-31 


43-50 
43-76 


43-66 


4415 

44-82 


44-63 


45-48 
45-95 


46-21 


46-6 
49-0 


48-5 
54-6 


27 


45-25 




44-04 




46-39 




49-02 




51-5 


53-8 


June 3 


45-22 




44-38 




47-18 




49-01 




51-9 


54-6 


10 
17 


45-21 
45-24 


45-23 


44-79 
45-21 


44-99 


48-10 
48-72 


48-40 


50-00 
50-99 


50-52 


49-5 
55-4 


53-1 
62-0 


24 


45-26 




45-60 




49-59 




52-10 




53-4 


54-3 


July 1 . . . 


45-31 




46-03 




50-58 




53-45 




55-9 


60-8 


8 


45-37 




4646 




51-28 




53-58 




51-9 


55-6 


15 


45-45 


45-47 


46-94 


46-85 


51-16 


50-97 


52-48 


52-76 


52-7 


55-0 


22 


45-54 




47-28 




50-90 




51-82 




526 


56-8 


29 


45-66 




47-56 




50-94 




52-48 




56-2 


60-0 


Aug. 5 . . . 


45 77 




47-73 




51-82 




54-00 




54-8 


54-2 


12 

19 


45-89 
46-02 


45-95 


48-02 
48-28 


48-12 


51-82 
51-70 


51-69 


52-90 
52-82 


52-88 


51-8 
54-2 


54-3 
56-8 


26 


46-13 




48-47 




51-41 




5180 




49-5 


52-8 


Sept. 2 


46 -27 




48-61 




51-28 




52-10 




53-1 


54-6 


9 


4639 




48-72 




51-43 




52-35 




55-8 


60-9 


16 


46-50 


46-49 


48-78 


48-79 


51-78 


51-04 


52-70 


51-18 


49-8 


50-3 


23 


46-59 




48-88 




51-00 




49-90 




42-8 


44-9 


30 


46-71 




48-94 




49-69 




48-87 




47-2 


48-3 


Oct. 7 


46-81 




48-82 




49-10 




48-25 




47*5 


49-0 


14 

21 


46-92 
47-00 


46-95 


48-66 
48-49 


48-56 


48 35 
47-90 


48-22 


46-98 
47-21 


47-11 


44-2 
47-3 


45-0 
48-0 


28 


47-07 




48-28 




47-51 




46-00 




42-0 


42-6 


Nov. 4 . . . 


47-12 




48-08 




46-90 




45-55 




43-0 


41-9 


11 

18 


47-19 
47-20 


47-18 


47-91 
47-72 


47-82 


46-75 
46-90 


4677 


46-55 
45-85 


45-86 


47-2 
43-7 


48-3 
45-3 


25 


47-20 




47-57 




46-51 




45-49 




40-7 


39-3 


Dec. 2 . . . 


47-21 




47-44 




45-10 




42-75 




40-5 


41-0 


9 . . . 


47-24 




47-20 




44-15 




41.80 




45-2 


49-7 


16 


47-22 


47-20 


46-88 


46-87 


43-55 


43-91 


41-30 


41-75 


42-4 


45-4 


23 


47-18 




46-55 




43-55 




41-60 




38-7 


40-9 


30 


47 14 




46-28 




43-20 




41-30 




36-2 


37-0 


1890. 






















Jan. 6 


47-11 




46-04 




42-90 




41-20 




41-2 


44-8 


13 

20 


47-05 
46-97 


47*01 


45-78 
45-58 


45-71 


43-10 
43-40 


42-95 


42-40 
42-60 


41-72 


43-0 
36-9 


44-7 
36-8 


27 


46-90 




45-45 




42-40 




40-70 




37-4 


38-8 


Feb. 3 . . . 


46-85 




45-27 




42-30 




41-50 




41-8 


45-1 


10 
17 


46-76 
46-69 


46-73 


45-06 
44-88 


44-96 


42-10 
41-00 


41 -52 


40-00 
38-70 


39-85 


35-4 
37-2 


35-9 
41-0 


24 


46-62 




44-64 




40-70 




39-20 




40-7 


43-4 


Mar. 3 


46-52 




44-37 




40-70 




38-80 




32-5 


33-0 


10 


46-46 




44-17 




40-70 




39-30 




40-7 


47-9 


17 


46-36 


46-36 


43-98 


44-07 


41-55 


41-39 


41-70 


40-68 


40-8 


41-0 


24 


46-28 




43-91 




41-80 




41-20 




40-2 


43-4 


31 


46-19 




43 -90 




42-20 




42-40 




41-5 


43-9 



OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 

Table I. — continued. 



161 



Date. 


! 


l 


k 


h 


t 


4 


k 


Air. 


















Surface 






Each 


Monthly 


Each 


Monthlj 


Each 


Monthl) 


Each 


Monthly 


Theorem. 


Each 




Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Each 
Reading. 


Reading. 


1890. 






















April 7 


46-11 




43-91 




42-75 




43-19 




43-2 


44-7 


14 
21 


46-02 
45-97 


46-00 


43-97 
44-02 


43-98 


42-75 
42-60 


42-79 


41-90 
42-08 


42-53 


39-2 
44-8 


43-9 

50-3 


28 


45-89 




44-03 




43-05 




42-95 




41-5 


44-1 


May 5 . . . 


45-83 




44-08 




43-80 




44-75 




46-4 


48-2 


12 
19 


45-80 
45-75 


4578 


44-19 
44-38 


44-31 


44-48 
45-11 


44-88 


45-09 
46-30 


46-05 


46-7 
48-6 


51-2 

48-5 


26 


4573 




44-58 




46-14 


1 


48-05 




47-9 


50-8 


.lime 2 . . . 


45-70 




44-84 




46-65 




47-58 




49-3 


52-0 


9 


45-69 




45-13 




47-35 




48-85 




53-0 


58-1 


It) 


45-68 


45-70 


45-43 


45-44 


48-01 


47-97 


49-29 


49-42 


55-3 


58-9 


23 


45-70 




4574 




48-61 




50-50 




54-4 


57-6 


30 


45-74 




46-05 




49-23 




50-86 




52-4 


54-2 


July 7 


45-77 




46-36 




49-20 




50-25 




50-4 


53-8 


14 
21 


45-82 
45-90 


45-87 


46-63 
46-86 


4673 


49-36 
49-98 


49-78 


50-57 
51-70 


51-27 


55-1 
56-8 


56-7 
62-5 


28 


45-97 




47-08 




50-59 




52-55 




54-9 


58-1 


Aug. 4 . . . 


46-05 




47-38 




51-10 




53-17 




58-3 


62 9 


11 

18 


46-12 
46-19 


46-16 


47-63 
47-95 


4779 


51-78 
51-70 


51-49 


53-80 
52-76 


52-88 


55-6 
53-0 


55-9 
55-9 


25 


46-28 




48-22 




51-40 




51-79 




50-3 


53-2 


Sept. 1 


46-38 




48-39 




50-61 




50-30 




49-4 


52-0 


8 


46-52 




48-50 




50-85 




52-19 




55-6 


60-3 


15 


46-62 


46-61 


48-55 


48-58 


51-23 


51-11 


52-33 


51-97 


54-7 


58-4 


22 


46-72 




48-66 




51-47 




52-51 




53-5 


57-5 


29 


46-81 




48-78 




51-37 




52-51 




52-8 


54-6 


Oct. 6 . . . 


46-90 




48-89 




50-88 




51-34 




51-5 


52-6 


13 
20 


47-00 
47-06 


47-02 


48-95 
48-92 


48-90 


50-58 
49-95 


50-13 


51-16 

48-68 


49-75 


52-3 
44-0 


53-9 
43-8 


27 


47-13 




48-84 




49-12 




47-81 




37-2 


36-7 


Nov. 3 


47-22 




48-70 




47-88 




40-59 




40-3 


39-0 


10 
17 


47-30 
47-37 


47-32 


48-48 
48 20 


48-32 


47-02 
46-10 


46-77 


45-15 
44-29 


45-33 


39-4 
40-6 


40-7 
40-7 


24 


47-41 




47-88 




4610 




45-28 




39-9 


39-0 


Dec. 1 . . . 


47-47 




47-65 




44-85 




41-80 




44-8 


51-2 


8 . . . 


47-44 




47-32 




44-40 




42-20 




36-9 


36-9 


15 


47-43 


47-41 


47-02 


46-98 


43-45 


43-33 


40-50 


40-58 


36-0 


38-9 


22 


47-38 




46-65 




42-35 




39-20 




32-0 


32-1 


29 '. 


47-35 




46-28 




41-60 




39-20 




34-2 


33-8 


1891. 






















Jan. 5 . . . 


47-30 




45-88 




41-20 




39-10 




33-1 


33-3 


12 
19 


47-27 
47-15 


47-20 


45-52 
45-14 


45-34 


40-60 
40-70 


40-68 


38-30 
38-40 


38-52 


40-8 
32-9 


44-9 
34-0 


26 


47-09 




44-84 




40-20 




38-30 




39 8 


44-4 


Feb. 2 . . . 


46-99 




44-54 




40-80 




39-90 




41-7 


467 


9 . . . 
16 


46-87 
46-77 


46-82 


44-35 
44-27 


44-34 


41-50 
41-55 


41-39 


41-20 
40-80 


40-62 


37-2 
41-0 


38-4 
43-2 


23 


46-67 




44-22 




41-70 




40-60 




40-0 


43-2 


Mar. 2 . . . 


46-55 




44-17 




41-60 




41-00 




43-1 


43-4 


9 


46-42 




44-08 




41-75 




40-30 




31-6 


30-7 


16 


46-34 


46-35 


44-04 


43-95 


40-60 


40-85 


38-50 


39-56 


36-4 


38-3 


23 


46-27 




43-85 




40-10 




38-90 




38-4 


41-3 


30 . 


46-18 




43-62 




40-20 




39-10 




34-6 


36-3 



162 



MR THOMAS HEATH ON 



Table I. — continued. 



Date. 


t 


l 


t 


2 


t 


» 


t 


i 


h 


Air. 








i 










Surface 






Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Theorem. 


Each 




Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Each 
Reading. 


Reading. 


1891. 






















April 6 


46-10 




43-45 




40-20 




39-10 




37-6 


37-6 


13 
20 


46-04 
45-95 


45-98 


43-31 
43-22 


43-30 


40-40 
41-10 


40-90 


40-00 
41-20 


40-68 


38-7 
39-9 


41-8 
40-8 


27 


45-84 




43-21 




41-90 




42-40 




42-4 


45-9 


May 4 


45 77 




43-27 




42-60 




42-90 




42-3 


46-6 


11 
18 


45-70 
45-62 


45-66 


43-42 
43-60 


43-53 


43-15 

44-08 


43-51 


43-93 
44-30 


44-03 


46-2 
42-8 


50-0 
45-4 


25 


45-57 




43-84 




44-20 




45-00 




44-8 


46-2 


June 1 


45-53 




44-04 




44-65 




45-67 




46-8 


46-3 


8 


45-50 




44-24 




45-20 




45-88 




46-4 


48-0 


15 


45-49 


45-50 


44-47 


44-51 


46-00 


46-44 


48-00 


48-32 


50-9 


54-3 


22 


45-49 




44-73 




47-51 




50-65 




53-7 


56-5 


29 


45-50 




45-09 




48-83 




51-41 




57-1 


62-2 


July 6 . . . 


45-49 




45-53 




49-62 




51-70 




54-7 


59-1 


13 
20 


45-53 
45-59 


45-57 


45-99 
46-40 


46-18 


49-98 
50-68 


50-36 


52-01 
53-26 


52-56 


56-3 
57-2 


61-5 
60-0 


27 


45-66 




4679 




51-18 




53-27 




55-0 


56-0 


Aug. 3 . . . 


4574 




47-15 




51-11 




52-68 




53-6 


55-5 


10 


45-83 




47-46 




51-17 




52-70 




53-4 


55-0 


17 


45-93 


45-94 


47-72 


47-69 


51 -29 


51-27 


52-75 


52-48 


53-6 


55-8 


24 


46-04 




47-95 




51-48 




52-68 




52-7 


55-3 


31 


46-15 




48-15 




51-28 




51-59 




51-4 


55-9 


Sept. 7 . . . 


46-25 




48-31 




50-81 




51-28 




50-2 


53-5 


n 

21 


46-37 
46-47 


46-42 


48-42 
48-46 


48-45 


50-99 
51-15 


50-86 


52-73 
51-92 


51-63 


56-3 

46-8 


55-7 
46-7 


28 


46-60 




48-62 




50-50 




50-58 




51-7 


56-3 


Oct. 5 . . . 


46-70 




48-64 




50-18 




50-30 




51-0 


52-6 


12 

19 


46-79 
46-88 


46-83 


48-63 
48-59 


48-58 


49-90 
49-00 


49-29 


49-59 
47-75 


48-56 


47 6 

46-4 


49-2 
48-2 


26 


46-97 




48-48 




48-10 




46-59 




44-6 


47-0 


Nov. 2 . . . 


47-04 




48-29 




47-15 




45-22 




447 


46-4 


9 . . . 


47-10 




48-06 




46-63 




45-30 




42-5 


44-8 


16 


47-15 


47-13 


47-80 


4779 


45-98 


45-86 


44"27 


43-99 


41-8 


43-7 


23 


47-16 




47-52 




45-35 




43-60 




36-6 


34-9 


30 


47-18 




47-26 




44-19 




41-55 




37-7 


39-7 - 


Dec. 7 


47-19 




46-94 




44-05 




43-00 




39-4 


39-0 


14 

21 


47-19 
47-17 


47*17 


46 63 
46-34 


46-48 


43-65 
42-65 


43-09 


41-10 
40-70 


41-22 


36-2 
37-9 


36-9 
38 4 


28 


47-12 




46-02 




42-00 




40-10 




37-1 


37-0 


1892. 






















Jan. 4 


47-06 




45-67 




41-60 




39-60 




32-9 


31-9 


11 
18 


46-99 
46-93 


46-96 


45-34 
45-01 


45-16 


40-90 
40-00 


40-58 


38-00 
37-00 


38-15 


31-8 
34-6 


31-0 
37-3 


25 


46-84 




44-64 




39-80 




38-00 




36-6 


39-1 


Feb. 1 


46-75 




44-29 




40-60 




40-30 




40-9 


41-3 


8 


46-66 




44-10 




40-50 




39-20 




40-2 


42-4 


15 


46 -54 


46-54 


43-96 


43-98 


41-10 


40-52 


40-50 


39-28 


36-2 


34-9 


22 


46-44 




43-85 




40-40 




37-90 




31-9 


34-9 


29 


46-31 




43-68 




40-00 




38-50 




35-7 


35-8 


Mar. 7 


46-20 




43-44 




39-60 




37-50 




33-0 


33-0 


14 
21 


46-09 
46-01 


46-05 


43-25 
42-99 


43-11 


39-00 
39-30 


39-48 


37-00 
39-20 


38-18 


31-8 
36-7 


32-5 
38-3 


. . . . 


45-91 




42-78 




40-00 




39-00 




32-2 


32-9 



OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 
Table I. — continued. 



163 





Date. 


i 


l 


l 




i 


3 


I 


4 


h 


Air. 




















Surface 








Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Theorem. 


Each 






Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Each 


Reading. 






— - 
















Reading. 






1892. 




















April 4 . . . 


45-80 




42-69 




39-90 




40-10 




41-9 


46-0 




11 

18 


45-70 
45-60 


45-65 


42-65 
4271 


42-70 


41-00 
40-80 


40-74 


41-10 
39-70 


40-75 


40-3 
35-5 


41-9 
38-4 




25 


45-51 




42-74 




41-25 




42-10 




43-2 


46-2 




May 2 . . . 


45-43 




42-82 




41-85 




41-90 




43-6 


48-9 




9 . . . 


45-35 




42-94 




42-45 




43-10 




46-7 


51-8 




16 


45-30 


45-30 


43-09 


43-17 


43-70 


43-57 


45-65 


44-63 


477 


50-8 




23 


45-24 




43-34 




44-45 




45-10 




45-8 


50-2 




30 


45-20 




43 66 




45-40 




47-42 




52-3 


59-4 




June 6 . . . 


45-16 




43-98 




46-50 




48-17 




50-8 


55-3 




13 
20 


45-15 
45-13 


4515 


44-34 
44-76 


44-55 


47-60 
47-42 


47-35 


49-09 
48-25 


48-78 


44-7 
47-4 


46-8 
49-1 




27 . 


45-17 




45-11 




47-86 




49-61 




55-4 


59-2 




July 4 


45-20 




45-40 




48-87 




50-93 




52-7 


52-2 




11 

18 


45-24 
45-31 


45-29 


45-74 
46-07 


45-90 


49-22 
49-45 


49-33 


50-88 
50-96 


51-14 


52-3 
51-6 


52-0 
52-9 




25 


45-40 




46-38 




49-78 




51-80 




54-9 


54-5 




Aug. 1 


45-49 




46-66 




50-45 




52-53 




56-8 


58-5 




8 


45-56 




46-94 




50-90 




52-48 




51-3 


50-0 




15 


45-65 


45-67 


47-28 


47-23 


50-72 


50-87 


52-29 


52-44 


54-7 


58-6 




22 


45-78 




47-54 




50-93 




52-39 




59-4 


64-4 




29 


45-88 




47-71 




51-37 




52-49 




49-5 


51-0 




Sept. 5 . . . 


45-98 




47-97 




50-78 




50-69 




48-2 


52-0 




12 
19 


46-10 
46-22 


46-16 


48-10 
48-15 


48-10 


50-26 
50-20 


50-25 


50-58 
50-55 


50-35 


51-6 

52-4 


55-3 
55-9 




26 


46-32 




48-18 




49-76 




49-59 




49-5 


54-3 




Oct. | 3 


46-40 




48-15 




49-08 




48-00 




46-1 


48-6 




10 


46-51 




48-11 




48-30 




47-10 




44-2 


46-2 




17 


46-58 


46-57 


47-95 


47-90 


47-48 


47-29 


46-19 


45-90 


40-3 


40-5 




24 


46-65 




47-76 




46-33 




44-05 




37-9 


37-3 




31 


46-72 




47-53 




45-26 




44-16 




41-7 


42-9 




Nov. 7 . ■ . 


46-77 




47-21 




45-09 




44-20 




417 


42-9 




14 . . . 
21 


46-80 
46-81 


46-80 


46-94 
46-75 


46-87 


45-20 
44-90 


44-86 


44-50 
43-05 


43-59 


42-8 
41-4 


42-3 
42-0 




28 


46-83 




46-59 




44-25 




42-60 




45-5 


50-3 




Dec. 5 


46-78 




46-32 




43-45 




40-30 




31-4 


28-8 




12 
19 


46-76 
46-77 


4675 


46-06 
45-69 


45-84 


4190 
41-55 


42-21 


38-90 
40-80 


39-92 


35-8 
43-0 


36-8 
44-8 




26 


46-69 




45-28 




41-95 




39-70 




31-5 


29-4 




1893. 
























Jan. 2 . . j 


46-63 




45-04 




40-64 




37-75 




31-5 


28-2 




9 


46-57 




44-72 




39-80 




36-70 




317 


34-3 




16 


46-50 


46-50 


44-35 


44-36 


39-20 


39-88 


36-70 


37-81 


35-2 


38-8 




23 


46-44 




43-99 




39-50 




38-30 




42-9 


47-3 




30 


46-34 




43-69 




40-25 




39-60 




41-8 


47-1 




Feb. 6 


46-83 




43-52 




40-80 




40-40 




39-7 


43-0 




13 
20 


46-10 
46-03 


46-06 


43-45 
43-41 


43-42 


41-00 
40 70 


40-80 


40-10 
40-35 


39-91 


34-4 
43-0 


33-5 
44-9 




27 


45-90 




43-32 




40-70 




38-80 




33-2 


34-8 




Mar. 6 


45-80 




43-24 




39-90 




39-20 




42-9 


45-7 




13 

20 


45-71 
45-64 


45-67 


43-05 
43-02 


43-08 


40-85 
40-90 


40-69 


40-90 
39-40 


40-21 


41-8 
39-9 


43-8 
46-3 


2/ . . 


45-54 




43-02 




41-10 




41-35 




41-0 


41-0 



164 



MR THOMAS HEATH ON 



Table I. — continued. 



Date. 


h 


t 


i 


t 


! 


t 


i 


h 


Air. 


















Surface 






Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Theorem. 


Each 




Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Each 
Reading. 


Reading. 


1893. 






















April 3 . . . 


45-47 




42-98 




41-60 




42-05 




45-1 


49-3 


10 
17 


45-39 
45-32 


45-36 


43-04 
43-13 


43-11 


42-40 
42-80 


42-52 


42-75 
43-05 


43-01 


42-7 
38-4 


43-9 
39-6 


24 


45-25 




43-28 




43-30 




44-20 




44-9 


49-1 


May 1 . . . 


45-19 




43-44 




44-20 




45-09 




43-0 


46-0 


8 


45-17 




43-69 




44-60 




45-95 




47-5 


487 


15 


45-14 


45-15 


43-93 


43-97 


45-69 


45-73 


47-98 


47-41 


51-3 


52-1 


22 


45-12 




44-23 




46-66 




48-44 




50-7 


55-5 


29 


45-12 




44-57 




47-48 




49-61 




50-7 


48-1 


June 5 . . . 


45-14 




44-94 




47-99 




49-85 




52-8 


57-4 


12 
19 


45-14 

45-20 


45-18 


45-29 
45-67 


45-50 


4876 
49-95 


49-38 


50-90 
53-67 


51-64 


54-7 
62-5 


58-5 
67-4 


26 


45"25 




46-10 




50-84 




52-15 




51-2 


54-4 


July 3 . . . 


45-32 




46-56 




50-80 




52-81 




56-6 


57-8 


10 


45-40 




46-90 




51-10 




53-10 




56-0 


58-8 


17 . . . 


45-50 


45-51 


47-22 


47-20 


51-26 


51-25 


52-70 


52-92 


53-9 


57-0 


24 


45-62 




47-54 




51-50 




53-06 




57-9 


62-4 


31 


45-73 




47-77 




51-59 




52-95 




53-1 


57-0 


Aug. 7 


45-85 




48-01 




51-52 




52-47 




54-5 


58-0 


14 
21 


45-99 
46-10 


46-04 


48-25 
48-45 


48-37 


52-20 
53-39 


52-55 


54-56 

56-20 


54-33 


60-5 

58-7 


65-9 
60-8 


28 


46-22 




48-76 




53-10 




54-09 




52-4 


55-8 


Sept. 4 . . . 


46-35 




49-05 




52-70 




53-88 




55-2 


59-1 


11 
18 


46-46 
46-58 


46-52 


49-17 
49-30 


49-20 


52-51 
51-89 


52-02 


52-61 
52-40 


52-15 


48-4 
53-4 


51-3 
56-7 


25 


46-69 




49"28 




51-00 




49-72 




45-0 


44-6 


Oct. 2 


46-83 




49-28 




50-01 




49-20 




48-4 


52-6 


9 


46-94 




49-12 




4920 




48-18 




44-8 


46-6 


16 


47-06 


47*04 


48-97 


48-95 


48-69 


49-09 


48-39 


48-42 


53-4 


56-7 


23 


47-15 




48-76 




49-04 




49-21 




47-0 


49-0 


30 


47-20 




48-62 




48-51 




47-12 




38-9 


38-9 


Nov. 6 . . . 


47-26 




48-50 




46-92 




44-00 




36-5 


37-0 


13 
20 


47-31 
47-34 


47-32 


48-22 
47-85 


48-02 


45-60 
45-05 


45-41 


43-60 
42-51 


43-03 


40-0 
46-6 


41-0 
37-8 


27 


47-37 




47-50 




44-06 




42-00 




37-6 


42-8 


Dec. 4 . . . 


47-39 




47-16 




44-17 




42-09 




42-9 


47-0 


11 

18 


47-35 

47-32 


47-34 


46-83 
46-59 


46-72 


43-94 
43-10 


43-56 


4171 
42-00 


41-90 


37-0 
41-5 


37-9 
44-7 


25 


47-28 




46-29 




43-05 




41-80 




40-3 


40-4 


1894. 






















Jan. 1 


47-21 




46-03 




43-30 




42-61 




37-8 


36-1 


8 


47-13 




45-81 




42-40 




39-20 




30-7 


30-8 


15 


47-08 


47-07 


45-60 


45-60 


41-59 


42-23 


40-49 


40-69 


38-6 


37-9 


22 


47-00 




45-48 




42-10 




41-15 




38-1 


39-1 


29 


46-93 




45-08 




41-75 




40-00 




34-4 


35-1 


Feb. 5 


46-85 




44-87 




41-21 




40-02 




39-0 


40-0 


12 
19 


46-75 
46-65 


46-70 


44-64 
44-46 


44-56 


41-71 
41-05 


41-17 


40-60 
39-04 


39-69 


38-3 
33-0 


38-1 
33-0 


26 


46-57 




44-27 




40-70 




39-09 




38-2 


43-9 


Mar. 5 


46-45 




44-05 




40-79 




39-61 




37-2 


39-0 


12 
19 


4636 
46-28 


46-31 


43-86 
43-74 


43-81 


40-89 
40-60 


40-94 


39-99 
39-50 


40-18 


36-6 
43-9 


39-1 

487 


26 


46-17 




43-61 




41-50 




41-60 




41-2 


43-9 



OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 



165 



Table I. — continued. 



Date. 


t 


l 


t 


2 


t 


3 


t 


4 


h 


Air. 


















Surface 






Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Theorem. 


Each 




Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Each 
Reading. 


Reading. 


1894. 






















April 2 . . . 


46-08 




43-60 




42-00 




42-50 




43-1 


44-3 


9 . . . 


45-99 




43-62 




42-51 




42-44 




42-0 


44-0 


16 


45-91 


45-91 


43-70 


43-75 


43-15 


43-07 


43-60 


43-54 


44-8 


47-3 


23 . 


45-82 




43-83 




43-67 




44-29 




43-8 


44-6 


30 . . . 


4577 




43-99 




44-03 




44-89 




477 


50-1 


May 7 . . • 


45-69 




44-13 




44-52 




44-79 




44-4 


46-8 


14 

21 


45 -5U 
45-60 


45-59 


44-31 
44-46 


44-37 


44-79 
44-89 


44-78 


45-51 
44-59 


45-06 


45-2 
40-5 


45-9 
42-8 


28 


45-58 




44-59 




44-93 




45-37 




43-6 


43-8 


June 4 . . . 


45-59 




44-74 




45-35 




46-28 




48-4 


49-5 


11 

18 


45-57 
45-57 


45-58 


44-87 
45-09 


45-01 


46-10 
47-22 


46-69 


47-39 
49-30 


48-24 


49-0 

50-7 


52-3 
540 


•25 


45-58 




45-35 




48-10 




49 97 




51-4 


51-8 


July 2 


45-60 




45-70 




49-21 




52-00 




56 3 


58-9 


9 . . . 


45-65 




46-20 




50-44 




53-06 




55-6 


59-1 


16 


45-68 


4570 


46-52 


46-52 


50-75 


50-51 


52-76 


52-69 


54-1 


55-0 


23 


4575 




46-92 




50-96 




52-54 




53-5 


57-6 


30 


45-82 




47-26 




51-20 




53-10 




54-9 


57-0 


Aug. 6 


45-91 




47-57 




51-80 




53-50 




54-9 


58-4 


13 
20 


46-02 
46-11 


46-07 


47-89 
48-15 


47-99 


51-84 
51-60 


51-61 


53 29 
52-34 


52-67 


54-3 
51-6 


58-0 
55-9 


27 


46-23 




48-36 




51-19 




51-55 




51-0 


54-0 


Sept. 3 . . . 


46-34 




48-46 




51-02 




51-55 




48-9 


50-2 


10 

17 . . . 


46-46 
46-55 


46-51 


48-55 

4857 


48-54 


50-54 
50-37 


50-59 


50-35 
5100 


50-89 


49-0 
611 


52-0 
512 


24 


46-68 




48-60 




50-44 




50 66 




49-9 


50-5 


Oct. 1 


46-78 




48-62 




49 91 




49-40 




48-4 


50-5 


8 . . . 


46-86 




48-61 




49-48 




49-09 




48-7 


50-4 


15 . 


46-93 


46-93 


48-55 


48-52 


49-40 


48-86 


49-26 


47-85 


44-5 


46-0 


22 


47-00 




48-46 




48-34 




46-29 




39-0 


41-0 


29 


47-09 




48-35 




47-15 




45-22 




42-9 


46-0 


Nov. 5 


47-15 




48-11 




47-00 




46-75 




48-6 


51-4 


12 
19 


47-19 
47-24 


47-20 


47-88 
47-75 


47-82 


47-06 
46-37 


46-61 


46-00 
44-90 


45-57 


43-1 
45-0 


45-0 
47-0 


26 


47-23 




47-54 




46-00 




44-64 




40-6 


40-0 


Dec. 3 


47-25 




47-34 




45-39 




43-89 




38-4 


361 


10 


47"27 




47-15 




44-71 




42-64 




43-1 


48-9 


17 . . . 


47-25 


47-23 


46-90 


46-90 


44-81 


44-56 


43 49 


42-78 


39-2 


44-5 


24 


47-22 




46-67 




44-10 




42-40 




40-7 


41-8 


31 


47-17 




46-45 




43-81 




4150 




33 


32-0 


1895. 






















Jan. 7 . . . 


47-13 




46-22 




42-39 




39-21 




329 


34-0 


14 
21 


47-09 
47-02 


47-05 


45-90 
45-46 


45-65 


41-06 
40-30 


40-91 


37-50 
37-85 


37-89 


317 
32-4 


36 1 
32-4 


28 


46-94 




45-01 




39-91 




37-00 




31-2 


26-0 


Feb. 4 


46-89 




44-61 




39-20 




36-40 




31-8 


35-0 


11 
18 


46-76 
46-67 


46 72 


44-20 
43-83 


44-01 


38-56 
37-59 


37-84 


35-25 
35-30 


35-49 


25-2 
30-8 


25-0 
30-9 


25 


46-56 




43-40 




36-00 




35-00 




31-7 


33-3 


Mar. 4 


46-44 




42-91 




36 00 




35-06 




31-9 


36-1 


11 

18 


46-30 
46-16 


46*23 


42-66 
42-42 


42-56 


3850 
38-30 


38-07 


37-00 
38-60 


37*71 


35-1 
39-5 


35-0 
42-8 


25 


46 02 




42-25 




39-50 




40-20 




40-2 


41-6 



VOL. XL. PART I. (NO. 8). 



2 A 



166 



MR THOMAS HEATH ON 
Table I . — continued. 



Date. 


h 


k 


t 


» 


t. 


i 


h 


Air. 


















Surface 






Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Theorem. 


Each 




Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Each 


Reading. 




















Reading. 





1895. 


















April 1 . 


45-85 




42-25 




40-00 




39-40 




38-1 


39-0 


8 . 


45-70 




42-32 




40-10 




39-50 




37 1 


41-0 


15 . 


45-57 


45-59 


42-35 


42-39 


40-70 


40-96 


40-90 


41-16 


39-9 


41-2 


22 . 


45-47 




42-42 




41-29 




42-28 




48-5 


53-8 


Tuesday 30 . 


45-35 




42-59 




42-71 




43-70 




46-2 


50-0 


May 6 . 


45-27 




42-80 




43-34 




44-50 




47-5 


50-0 


13 . 
20 . 


45-21 
45-12 


45-17 


43-08 
43 35 


43-25 


44-48 
45-20 


44-59 


46-46 
45-89 


45-81 


52-8 
43-7 


59-0 
45-1 


27 . 


45-09 




43-77 




45-35 




46-40 




51-6 


59-5 


June 3 . 


45-06 




44-06 




46-67 




49-18 




51-3 


52-4 


10 . . . 
17 . 


45-07 
45-07 


45-07 


44-42 
44-84 


44-65 


47-85 
48-32 


47-80 


50-60 
49-54 


49-85 


547 
49-6 


579 
52-0 


24 . 


45-09 




45-28 




48-36 




50-08 




54 1 


55-9 


July 1 . 


45-13 




45-61 




49-46 




51-69 




54-3 


57-8 


8 . 


45-20 




45-99 




50-15 




52-60 




59 


64-8 


15 . . . 


45-28 


45-29 


46-37 


46-36 


50-60 


50-33 


52-16 


52-06 


54-0 


57-9 


22 . . . 


45-38 




46-74 




50-70 




52-20 




54-2 


58-4 


29 . 


45-47 




47-08 




50-76 




51-61 




52-8 


54-7 


Aug. 5 . 


45-57 




47-33 




50-66 




51-75 




53-4 


54-5 


12. . . 

19 . 


45-68 
45-84 


45-76 


47-56 

47-78 


47-67 


50-95 
51-38 


51-25 


52-51 
53-49 


52-71' 


54-2 
58-9 


55-9 
61-4 


26 . 


45-95 




48-01 




52-03 




53-10 




52-7 


56-0 


Sept. 2 . 


46-08 




48-30 




51-84 




53-05 




55 1 


58-2 


9 . 


46-19 




48-50 




51-79 




52-70 




53-9 


57-0 


Tuesday 17 . 


46-35 


46-33 


48-69 


48-63 


51-69 


51-70 


52-51 


52-63 


55-4 


57-1 


23 . . ; . 


46-45 




48-78 




51-57 




51-89 




51-8 


56-4 


30 . ... 


46-58 




48-8S 




51-60 




52-98 




53-0 


54-9 


Oct. 7 . 


46-67 




48-94 




50-93 




49-84 




44-8 


46-0 


14 . 
21 . 


46-80 
46-88 


46-83 


49-00 
48-86 


48-86 


49-75 

48-80 


49-15 


49-09 

47-05 


47-49 


48-9 
41-1 


48-4 
39-2 


28 . 


46-98 




48-65 




47-12 




44-00 




35-7 


35-7 


Nov. 4 . 


47-09 




48-37 




45-75 




43-30 




40-2 


40-7 


11 . . . 

18 . 


47-18 
47-22 


47-18 


47-99 
47-60 


47-83 


45-65 

45-27 


45-41 


44-30 
43-45 


43-64 


44-2 
38-3 


45-9 
39-3 


25. 


47"25 




47-36 




44-96 




43-50 




40-2 


41-3 


Dec. 2 . 


47-27 




47-10 




44-75 




43-60 




40-1 


43-4 


9 . 


47-26 




46-87 




44-30 




41-75 




39-1 


44-6 


16 . 


47-22 


47-22 


46-63 


46-60 


43-30 


43-42 


41-20 


41-24 


36-5 


35-6 


23 . 


47-19 




46-34 




42-75 




40-25 




36-0 


37-0 


30 . 


47-16 




46-05 




42-00 




39-41 




39-5 


41-0 


1896. 






















Jan. 6 . 


47*11 




45-68 




42-36 




41-61 




39-5 


40-9 


13 . 

20 . 


47-04 
46-96 


47-01 


45-42 
45-24 


45-35 


42-25 
41-95 


42-09 


40-30 
41-00 


40-89 


36-4 
37-8 


36-5 
38-6 


27. ... 


46-91 




45-07 


• 


41-80 




40-63 




44-9 


50-8 


Feb. 3 . 


46-80 




44-87 




42-14 




41-09 




39-2 


43-3 


10 . 
17 . 


4672 
46-63 


46-67 


44-75 
44-65 


44-72 


42-33 
43-00 


42-59 


42-10 
42-94 


41-97 


42-8 
43-3 


44-5 
45-8 


24 . . . 


46-52 




44-62 




42-89 




4175 




347 


34-1 


Mar. 2 . 


46-45 




44-58 




42-05 




40-76 




38-5 


40-0 


9 . 


46-37 




44-49 




41-74 




40-49 




41-1 


42-5 


16 . 


46-29 


46-30 


44-35 


44-34 


41-80 


41-91 


40-40 


40-93 


39-5 


42-0 


Tuesday 24 . 


46-23 




44-18 




41-80 




41-50 




45-1 


49-5 


Monday 30 . 


46-14 




44-08 




42-15 




41-50 




37-2 


37-9 



OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 

Table I. — continued. 



167 





Date. 


h 


t 


2 


t 


i 


t 


i 


h 


Air. 


















Surface 








Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Theorem. 


Each 






Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Each 
Reading. 


Reading. 




1896. 




















April 


6 . 


46-09 




44-07 




42-30 




42-70 




47-3 


51-8 ' 




13 . 
20 . 


46-00 
45-94 


45-98 


44-06 
44-15 


44-12 


43-50 
43-44 


43-41 


43-59 
43-75 


43-90 


40-3 

48-0 


42-9 
52-5 




27 . 


45-87 




44-22 




44-40 




45-55 




49-0 


51-9 


May 


4 . 


45-82 




44-37 




44-75 




45-15 




47-7 


54-0 




11 . 
18 . 


45-79 
45-75 


45-77 


44-56 
4477 


44-71 


45-56 
46-90 


46-16 


47-24 
49-00 


47-61 


52-3 
52-7 


62-5 
54-6 




25 . 


4572 




45-16 




47-41 




49-05 


. 


51-4 


55-0 


June 


1 . 


45-71 




45-39 




48-34 




50-50 




52-4 


55-4 




8 . 


4571 




4574 




48-70 




49-59 




50-8 


53-2 




15 . 


45-74 


4575 


46-09 


46-06 


48-98 


49-28 


50-94 


51-12 


55-3 


58-0 




22 . . . 


45-76 




46-38 




50-00 




51-90 




52-9 


56-0 




29 . 


45-83 




46-69 




50-36 




52-65 




54-7 


57-5 


July 


6 . 


45-91 




47-02 




5070 




52-22 




57-3 


62-0 




13 . 
20 . 


45-98 
46-08 


46-03 


47-33 
47-62 


47-46 


50 98 

51 63 


51-30 


52-95 
53-85 


53-03 


57-6 
61-5 


61-3 
66-4 




27 . 


46-14 




47-88 




51-90 




53-10 




52-2 


53-9 


Aug. 


3 . 


46-25 




48*22 




51-70 




52-83 




54-7 


57-6 




10 . 


46-35 




48-40 




51-66 




52-69 




51-8 


55-9 




17 . 


46-46 


46-47 


48-56 


48-55 


51-77 


51-67 


52-85 


52-67 


52-8 


55-0 




24 . 


46-58 




4873 




51-74 




52-85 




55-6 


58-0 




31 . 


46-69 




48-86 




51-49 




52-14 




52-7 


55-0 


Sept. 


7 . 


46-80 




48-97 




51-60 




52-46 




52-3 


52-0 




14 . 
21 . 


46-92 
47-03 


46-97 


49-07 
49-13 


49-09 


51-64 
51 -00 


51-14 


52-54 
51-87 


51-61 


54-5 
51-7 


57-6 
53-0 




28 . 


47-12 




49-19 




50-30 




49-57 




46-8 


49-0 


Oct. 


5 . 


47-21 




49-11 




49-84 




49-62 




44-4 


44-1 


Tuesday 13 . 
Monday 19 . 


47-30 
47-39 


47 34 


48-97 
48-82 


48-86 


48-70 
47-60 


48-16 


46-50 
45-85 


46-45 


38-4 
42-5 


39-1 
42-1 




26 . 


47-45 




48-55 




46-50 




43-82 




37-6 


38-5 


Nov. 


2 . 


47-52 




48-24 




45-40 




43-10 




39-5 


40-3 




9 . 


47-55 




47-86 




44-70 




42-49 




36-3 


39-4 




16 . 


47-58 


47-55 


47-50 


47-55 


44-66 


44-76 


43-38 


43-12 


42-9 


44-5 




23 . 


47-60 




47-22 




44-47 




43 30 




47-9 


48-8 




30 . 


47-52 




46-94 




44-56 




43-35 




34-7 


31-0 


Dec. 


7 . 


47-51 




46-75 




43-91 




42-46 




40-0 


40-0 




14 . 
21 . 


47-46 
47-39 


47-42 


46-54 
46-30 


46-39 


43-70 
42-69 


43-04 


42-10 
39-74 


41-15 


37-5 
34-7 


37-6 
35-6 




28 . 


47-34 




45 99 




41-85 




40-30 




37-8 


37-5 




1897. 






















Jan. 


4 . 


47-28 




45-66 




42-21 




40-96 




40-7 


41-9 




11 . 

18 . 


47-19 

47-08 


47-13 


45-40 
45-16 


45-29 


42-09 
41-30 


41-52 


40-20 
38-80 


39-43 


35-0 
32-5 


35-8 
33-0 




25 . 


46-96 




44-92 




40-50 




37-75 




32-2 


38-1 


Feb. 


1 . 


46-86 




44-61 




39-70 




39-00 




32-0 


33-6 




8 . 
15 . 


46-76 
46-65 


46-70 


44-27 
43-95 


44-11 


39-10 
39-25 


39-56 


37-00 
37-99 


38-55 


36-4 
38-2 


40-6 
39-3 




22 . 


46-54 




43-63 




40-20 




40-20 




44-2 


48-7 


Mar. 


1 . 


46-37 




43-50 




41-40 




41-49 




39-2 


40-1 




8 . 


46-23 




43-45 




40-90 




39-80 




36-1 


36-3 




15 . 


46-10 


46*11 


43-42 


43-42 


40-80 


41-14 


39-70 


40-68 


36-2 


36-1 




22 . 


45-98 




43-29 




40-80 




40-50 




44-5 


48-7 




29 . 


45-85 




43-45 




41-82 




41-89 




36-5 


37-1 



168 



MR THOMAS HEATH ON 



Table I. — continued. 



Date. 


k 


t. 




h 


k 


k 


Air. 


















Surface 






Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Theorem. 


Each 




Reading 


MeaD. 


Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Each 
Reading. 


Reading. 


1897. 






















April 5 . . . 


45-74 




43-26 




41-00 




39-28 




35-5 


38-9 


12 
19 


45-65 
45-55 


45-60 


43-20 
43-13 


43-19 


40-66 
41-20 


41-14 


40-00 
41-15 


40-53 


42-0 

42-8 


47-0 
459 


'26 


45-45 




43-19 




41-70 




41-69 




43-3 


46-5 


May 3 


45-36 




43-10 




42-29 




42-88 




42-5 


43-6 


10 


45-33 




43-21 




42-80 




4338 




44-9 


49-0 


17 


45-25 


45-26 


43-36 


43-39 


43-23 


43-55 


44-26 


44-47 


48-5 


53-6 


24 


45-20 




43-52 




44-41 




45-72 




46-9 


48-1 


31 


45-16 




43-76 




45-02 




46-11 




51-4 


56-3 


June 7 


45-10 




44-05 




45-89 




47-83 




47-4 


47-7 


14 
21 


45-10 
45-09 


45-09 


44-33 
44-65 


44-50 


46-50 
47-09 


46-77 


48-80 
47-53 


48-47 


55-0 
50-1 


55-9 
56-9 


28 


45-09 




44-96 




47-60 




49-72 




52-7 


53-0 


July 5 


45-14 




45-26 




48-61 




50-72 




55-6 


60-2 


12 
19 


45-15 
45-22 


45-20 


45-60 
45-94 


45-78 


48-98 
49-91 


49-57 


50-63 
52-52 


51-79 


56-0 
56-5 


60-8 
61-9 


26 


45-28 




46 32 




50-77 




53-31 




56-1 


59-4 


Aug. 2 


45-37 




46-74 




51-36 




53-85 




58-6 


62-7 


9 


45-46 




47-13 




52-21 




54-88 




57-9 


61-9 


16 


45-55 


45-57 


47 -52 


47-48 


52-40 


51-99 


53-98 


53 79 


54-1 


57-7 


23 


45-67 




47-88 




52-06 




53-09 




54-5 


57-1 


30 


45-79 




48-15 




51-90 




53-14 




55-0 


58-1 


Sept. 6 . . . 


45 91 




48-33 




51-50 




51-31 




49-6 


52-6 


13 

20 


46-06 
46-16 


46-08 


48-48 
48-45 


48-42 


50-42 
50-31 


50-48 


49-90 
49-81 


50-16 


54-0 
47-6 


59-7 
52 


27 . 


46-19 




48-41 




49-70 




49-61 




49-5 


53-0 


Oct. 4 


46-40 




48-34 




49-60 




49-53 




46-9 


47-3 


11 

18 


46-49 
46-60 


46-54 


48-30 
48-25 


48-25 


49-23 
48-29 


48-88 


48-83 
47-58 


48-45 


47-0 
51-2 


49-7 
55-0 


25 


46-67 




48-10 




48-40 




47-86 




45 8 


48-0 


Nov. 1 


46-74 




47-99 




47-85 




47-30 




46"2 


46-7 


8 


46-79 




•47-86 




47-46 




47-41 




46-1 


48-8 


15 


46-81 


46-82 


47-70 


47-72 


47-39 


47-22 


47-30 


4676 


37 "5 


35-0 


22 


46-89 




47-61 




46-80 




46-51 




46-9 


48-9 


29 


46-88 




47-44 




46-60 




45-30 




377 


37-1 


Dec. 6 


46-92 




47-31 




45-22 




42-95 




41-9 


44-5 


13 
20 


46-91 
46-92 


46-92 


47-05 

46-75 


46-90 


44-45 
44-05 


44-24 


42-30 
42-60 


42-76 


36-6 
39-2 


38-2 
39-4 


27 . 


46-94 




46-50 




43-22 




43-20 




44-4 


37-9 


1898. 






















Jau. 3 


46-90 




46-18 




43-22 




41-82 




39-9 


39 1 


10 


46-87 




45-90 




43-13 




41-86 




39-6 


42-0 


17 


46-82 


46-82 


45-69 


45-75 


43-38 


43-47 


42-51 


42-60 


43-4 


48-1 


24 


46-79 




45-55 




43-71 




43-00 




43-3 


46-5 


31 


46-72 




45-45 




43-90 




43-82 




44-4 


45-0 


Feb. 7 


46-63 




45-36 




43-86 




42-00 




35-0 


36-0 


14 
21 


46-59 
46-52 


46-55 


45-67 
45-16 


45-30 


43-09 

42-80 


42-87 


41-98 
40-90 


41-67 


40-1 
32-7 


43-3 
30-9 


28 


46-47 




45-02 




41-73 




41-81 




39-6 


390 


Mar. 7 


46-42 




44-80 




41-25 




39-30 




35-1 


34-8 


14 
21 


46-37 
46-32 


46-34 


4456 
44-34 


44-49 


41-18 
42-00 


41-63 


40-39 
41-90 


40-55 


39-9 
39-4 


40-2 
42-5 


28 


46-23 




44-26 




42-10 




40-63 




36-3 


37-9 



OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 



169 



Table I.- — continued. 



Date. 


t 


i 


t 


2 


t 


3 


t 


i 


h 


Air. 


















Surface 






Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Theorem. 


Each 




Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Each 
Reading. 


Reading. 


1898. 






















April 4 


46-17 




44-19 




41-55 




40-10 




38-9 


42-0 


11 
18 


46-12 

46-05 


46-08 


44-09 
44 05 


44-11 


42-20 
42 98 


42-61 


42-90 
43-19 


42-60 


45-4 
446 


49-6 
49-8 


25 


45 98 




44-12 




43-70 




44-20 




44-6 


46-0 


May 2 . . . 


45-92 




44"23 




43-98 




44-23 




45-3 


47-2 


9 . . . 


45 86 




44-35 




44-45 




45-30 




49-1 


51-6 


16 


45-81 


45-83 


44-50 


44-50 


44-75 


44-70 


44-73 


45-21 


42-9 


45-8 


23 


4578 




44-64 




44-90 




45-40 




46-2 


46-9 


30 


45 76 




44-76 




45-43 




46-37 




461 


49-2 


June 6 . . . 


4576 




44-93 




45-79 




46 65 




50-3 


61-1 


13 
20 


45-74 
45-75 


45-75 


45-10 
45-37 


. 45-27 


47-09 

48-05 


47-41 


48-90 
50-30 


49-04 


49-9 
54-4 


51-0 
57-0 


27 . . . 


45-75 




45-69 




48-71 




50-32 




52-1 


52-5 


July 4 


45-77 




46-05 




49-39 




5114 




51-8 


55-2 


11 
18 


45-83 
45-86 


45-85 


46-39 
46-70 


46-55 


49-88 
50-64 


50-22 


52-02 
52 68 


52-19 


57-5 
56-1 


61-5 
59-0 


25 


45-93 




47 -05 




50-96 




52-92 




54"2 


58-8 


Aug. 1 . . . 


46-01 




47-36 




51-10 




52-63 




55-8 


58-8 


8 


46-07 




47-66 




51-39 




52-60 




53-2 


55-1 


15 


46-18 


46-20 


47 95 


47-91 


51-60 


51-60 


53-70 


53-07 


57-2 


59-0 


22 


46-38 




48-20 




51-91 




53 39 




57-5 


62-1 


29 


46-36 




48-38 




52-00 




53-02 




50-0 


52-0 


! Sept. 5 . . . 


46-51 




48-65 




51-61 




52-96 




599 


67-0 


12 . . . 
19 


46-59 
46-70 


46-65 


48-75 
48-95 


48-86 


52-49 
52-33 


52-05 


54-10 
53-88 


53-08 


527 
50-5 


54-0 
50-1 


26 


46-80 




49-10 




51-76 




51-39 




47 5 


48-4 


Oct. 3 . . . 


46-93 




49-22 




50-86 




50-94 




55-0 


57-1 


10 


47-02 




49-17 




50-96 




51-00 




49-2 


50-0 


17 . . . 


47-12 


47-12 


4914 


49-11 


51-16 


50-32 


50-06 


49-92 


45-3 


45-5 


24 


47-22 




49 09 




49-48 




49-15 




48-0 


50-0 


31 


47-30 




48-95 




49-15 




48-45 




46-6 


47-9 


Nov. 7 


47-40 




48-83 




48-50 




47-09 




46-0 


48-3 


14 
21 


47-46 
47-49 


47-46 


48 66 

48-44 


48-52 


47-70 
47-38 


47-39 


46-17 
46-20 


45-77 


43-2 
40-4 


45-9 
40-4 


28 


47-50 




48-17 




46-00 




43-63 




35-1 


33-0 


Dec. 5 . . . 


47-59 




47-95 




43-18 




43-68 




48-9 


54-0 


12 
19 


47-60 
47-56 


47-58 


47-61 
47-32 


47-51 


45-28 
45-25 


44-62 


44-12 
44-23 


43-88 


47-4 
39 4 


52-0 
39-1 


26 


47-55 




47-15 




44-78 




43-50 




46-0 


47-2 


1899. 






















Jan. 2 


47-50 




46-90 




44-40 




42-03 




36-5 


37-0 


9 

1 


47-49 




46-72 




43-53 




44-23 




42-2 


45-8 


16 


47-43 


47-42 


46-42 


46-40 


43-08 


43-12 


41-10 


41-55 


40-6 


42-0 


23 


47-36 




46-12 




42-72 




41-46 




35-9 


34-2 


30 


47-32 




45-83 




41-89 




38-95 




34-5 


35-9 


Feb. 6 


47-22 




45-52 




41-05 




38-22 




32 8 


33-1 


13 

20 


47-17 
47-08 


47-11 


45-19 
44-86 


45-06 


40-95 
41-57 


41-24 


40-28 
41-00 


39-76 


40-2 
38-3 


42-2 
390 


27 


46-97 




44-68 




41-39 




39-52 




32-7 


33-0 


Mar. 6 


46-88 




44-54 




41-29 




40-13 




38-9 


43-9 


13 

20 


46-79 
46-65 


46-72 


44-41 
44-26 


44-36 


41-39 
42-13 


41-47 


41-05 
41-52 


40-33 


43-2 
33-7 


48-0 
33-3 


27 


46-58 




44-25 




41-06 




38-63 




38-6 


45-7 



170 



MR THOMAS HEATH ON 



Table I. — continued. 



Date. 


k 


t 


2 


t 


i 


t 


> 


h 


Air. 


















Surface 




Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Each 


Monthly 


Theorem. 


Each 




Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Reading. 


Mean. 


Each 
Reading. 


Reading. 


1899. 






















April 3 . . . 


46-48 




44-09 




41-31 




41-19 




43-9 


49-2 


10 

17 -. 


46-37 
46-31 


46-35 


43-98 
43-97 


44-00 


42-12 
41-90 


41-78 


41-58 
41-03 


41-21 


39-4 
37-6 


39-0 
38-6 


24 


46-23 




43 96 




41-78 




41-05 




44 6 


52-1 


May 1 . . . 


46-13 




43-92 




4272 




43-02 




40-2 


39-4 


8 


46-07 




43-97 




42-98 




42-99 




44-0 


47-7 


15 


46-01 


46-00 


44-04 


44-OS 


43-62 


43-57 


44-01 


43-87 


44-7 


457 


22 


45-92 




44-14 




44-18 




44-50 




42-8 


43-1 


29 


45-89 




44-33 




44-34 




44-85 




49 9 


57-7 


June 5 


45-86 




44-47 




45-92 




48-31 




56-1 


61-6 


12 . . 
19 


45-84 
45-80 


45-83 


44-76 
45-16 


45-01 


. 47-68 
49-01 


48-04 


54-80 
51-80 


51-61 


57-9 
. 53-7 


68*9 

55-6 i 


26 


45-82 




45-66 




49-57 




51-55 




57-3 


62-2 


July 3 . . . 


45-83 




46-14 




50-03 




51-50 




54-5 


59-0 


10 


45-87 




46-55 




50-55 




53-02 




56-5 


57 3 


17 


45-93 


45-95 


46-93 


46-91 


51-05 


51-00 


53-16 


52-97 


58-3 


61-9 


24 


46-0) 




47-29 




51-52 




53-40 




57-6 


62-3 i 


31 


46-10 




47-64 




51-83 




5378 




61-2 


66-8 1 


Aug. 7 


46-19 




47-94 




52-58 




54-71 




54-4 


54-7 


14 
21 


46-30 
46-43 


46-36 


48-27 
48-60 


48-41 


52-55 
52-80 


52-83 


54-46 
54-29 


54-80 


58-1 
59-4 


60-0 
65-9 


28 


46-53 




48-84 




53-38 




55-74 




57-8 


59-8 


Sept. 4 . . . 


46-6« 




49-13 




53-26 




54-26 




57'2 


61-9 


11 

18 


46-78 
46-88 


46-83 


49-35 
49-48 


49-38 


52-97 
52-44 


52-51 


53-72 
52-65 


53-66 


55-0 
49-1 


62-0 
51-4 


25 


47-02 




49-56 




51-39 




54-00 




48-2 


51-0 


Oct. 2 


47-14 




49-53 




50-10 




48-85 




46-8 


49-2 


9 . . . 


47-27 




49-39 




49-42 




48-20 




47-7 


517 


16 


47-38 


47-36 


49-18 


49-19 


49-19 


49-16 


47-68 


48-03 


44-3 


487 


23 


47-47 




49-02 




4872 




47-85 




47-4 


50-1 


30 . 


47-52 




48-82 




48-38 




47-58 




45-2 


46-7 ' 


Nov. 6 . . . 


47-59 




48-64 




47-92 




47-02 




45-4 


48-6 


13 
20 


47-64 
47-65 


47-64 


48-48 
48-27 


48-37 


47-47 
46-87 


47-24 


45-89 
45-26 


46-09 


47-2 
44-3 


507 
43-6 


27 . . . 


47-69 




48-09 




46-69 




46-19 




48-8 


50-6 


Dec. 4 


47-69 




47-89 




46-93 




45-62 




46-6 


51-6 


11 

18 


47-65 
47-64 


47-65 


47-70 
47-53 


47-58 


46-13 
44-26 


45-16 


43-65 
41-02 


42-71 


33-7 
35-8 


32-4 
37-0 


25 


47-62 




47-19 




43-30 




40-55 




34-9 


34-5 



OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 



171 



Table II. — The Edinburgh Royal Observatory Rock Thermometers. 
Monthly, Quarterly, and Annual Means. 



Date. 


h 


h 


k 


k 




























Monthly. 


Quarterly. 


Annual. 


Monthly. 


Quarterly. 


Annual. 


Monthly. 


Quarterly. 


Annual. 


Monthly. 


Quarterly. 


Annual. 


1888. 


























January, . 


46-80 






44-84 






41-25 






39-78 






February, 


46 38 


46-39 




44-02 


43-98 




40-25 


40-26 




38-47 


38-67 




March, 


45-99 




46-03 


43-08 




45-28 


39-28 




44-54 


37-75 




44-20 


April, ; . 


45-54 






42-40 






39-S3 






39-67 






May, 


45-14 


45-22 




42-82 


43-11 




43-54 


43-19 




45-13 


44-11 




June, 


44-98 




45-88 


44-11 




45-18 


46-21 




44-76 


47-54 




44-60 


July, 


45-10 






45-57 






48-80 






50-34 






August, . 


45-45 


45-47 




46-87 


46-66 




49-94 


49-55 




51-12 


50-62 




i September, 


45-86 




45-84 


47-55 




45-28 


49-92 




44-98 


50-39 




44-86 


October, . 


46-26 






47-55 






47-68 






47-13 






November, 


46-50 


46-45 




47-06 


46-96 


' 


46-22 


46-02 




45-16 


44-98 




December, 


46-58 






46-28 






44-16 






42-65 






1889. 






45-88 






45-50 






45-40 






45-36 


1 January, . 


46-47 






45-23 






42-02 






40-62 






February, 


46-24 


46-22 




44-41 


44-41 




41-20 


41-14 




39-52 


39-74 




March, 


45-96 




46-00 


43-59 




45-81 


40-20 




45-82 


39-08 




45-78 


April, 


45-59 






43-23 






41-62 






41-61 






May, 


45-31 


45-38 




43-66 


43-96 




44-63 


44-88 




46-21 


46-11 




June, 


45-23 




46-17 


44-99 




46-01 


48-40 




45-89 


50-52 




4576 


July, 


45-47 






46-85 






50-97 






52-76 






August, . 


45-95 


45-97 




48-12 


47-92 




51-69 


51-23 




52 88 


52-27 




September, 


46-49 




46-29 


48-79 




46-14 


51-04 




46-09 


51-18 




46-01 


October, . 


46-95 






48-56 






48-22 






47-11 






November. 


47-18 


47-11 




47-82 


47-75 




46-77 


46-30 




45-86 


44-91 




December, 


47-20 






46-87 






43-91 






41-75 






1890. 






46-40 






46-29 






46-17 






45-98 


January, . 


47-01 






45-71 






42-95 






41-72 






February, 


46-73 


46-70 




44-96 


44-91 




41-52 


41-96 




39-85 


40-75 




March, . 


46-36 




46-46 


44-07 




46-24 


41-39 




46-06 


40-68 




45-92 


April, 


46-00 






43-98 






42-79 






42-53 






May, 


4578 


45-83 




44-31 


44-58 




44-88 


45-21 




46-05 


46-00 




June, 


45-70 




46-50 


45-44 




46-32 


47-97 




46-17 


49-42 




46-00 


July, 


45-87 






46-73 






49-78 






51-27 






August, . 


46-16 


46-21 




47-79 


47-70 




51-49 


50-79 




52-88 


52-04 




September, 


46-61 




46-52 


48-58 




46-22 


51-11 




45-93 


51-97 




45-71 


October, . 


47-02 






48-90 






50-13 






49-75 






November, 


47-32 


47-25 




48-32 


48-07 




4677 


46-74 




45-33 


45-22 




December, 


47-41 






46-98 






43-33 






40-58 






1891. 






46-49 






46-02 






45-53 






45-29 


January, . 


47-20 






45-34 






40-68 






38-52 






February, 


46-82 


46-79 




44-34 


44-54 




41-39 


40-97 




40-62 


39-57 




March, . 


46-35 




46-43 


43-95 




45-96 


40-85 




45-54 


39-56 




45-34 


April, 


45-98 






43-30 






40-90 






40-68 






May, 


45-66 


45-71 




43-53 


4378 




43-51 


43-62 




44-03 


44-34 




June, 


45-50 




46-38 


44-51 




45-84 


46-44 




45-38 


48 -32 




45-18 


July, 


45-57 






46-18 






50-36 






52-56 






August, . 


45-94 


45-98 




47-69 


47-44 




51-27 


50-83 




52-48 


52-22 




September, 


46-42 




46-31 


48-45 




45-73 


50-86 




45-18 


51-63 




44-92 


October, . 


46-83 






48-58 






49-29 






48-56 






November, 


47-13 


47-04 




4779 


47-62 




45-86 


46-08 




43-99 


44-59 




December, 


47-17 




46-23 


46-48 




45-65 


43-09 


i 


45-25 


41-22 




45-02 



172 



MR THOMAS HEATH ON 



Table II. — continued. 



Date. 




h 




k 




k 






h 




Monthly. Quarterly. 


Annual. 


Monthly. 


Quarterly. 


Annual. 


Monthly. 


Quarterly. 


Annual. 


Monthly. 


Quarterly. 


Annual. 


1892. 






















January, . 


46-96 






45-16 






40-58 






38-15 






February, 


46-54 


46-52 




43-98 


44-08 




40-52 


40-19 




39-28 


38-54 




March, 


46-05 




46-16 


43-11 




45-56 


39-48 




45-08 


38-18 


i 


44-79 


April, 


45-65 






42-70 






4074 






4075 






May, 


45-30 


45-37 




43-17 


43-47 




43-57 


43-89 




44-63 


44-72 




June, 


45-15 




46 08 


44-55 




45-37 


47-35 




44-76 


48-78 




44-43 


July, 


45-29 






45-90 






49-33 






51-14 






August, 


45-67 


45-71 




47"23 


47 08 




50-87 


50-15 




52-44 


51-31 




September, 


46-16 




45-97 


4810 




45-26 


50-25 




44-82 


50-35 




44-62 


October, . 


46-57 






47-90 






47-29 






45-90 






November, 


46-80 


46-71 




46-87 


46-87 




44-86 


44-79 




43 59 


4314 




December, 


46-75 




45-93 


45-84 




45-44 


42-21 




45-32 


39-92 




45-28 


1893. 


























January, . 


46-50 






44-36 






3988 






37-81 






February, 


46-06 


46-08 




43-42 


43-62 




40-80 


40-46 




39-91 


39-31 




March, 


45-67 




46-01 


43-08 




45-74 


40-69 




45-77 


40-21 




4573 


April, 


45-36 






43-11 






42-52 






43-01 






May, 


45-15 


45-23 




43-97 


44-19 




4573 


45-88 




47-41 


47-35 




June, 


45-18 




46-14 


45-50 




45-99 


49-38 




46-08 


51-64 




46-06 


July, 


45-51 






47-20 






51-25 






52-92 






August, . 


46-04 


46-02 




48-37 


48-26 




52-55 


51-94 




54-33 


53-13 




September, 


46-52 




46-29 


49-20 




46-25 


52-02 




46-32 


52-15 




46-28 


October, . 


47-04 






48-95 






49-09 






48-42 






November, 


47-32 


47-23 




48-02 


47-90 




45-41 


46-02 




43-03 


44-45 




December, 


47-34 




46-41 


46 72 




46-30 


43-56 




46-06 


41-90 




45-84 


1894. 


























January, . 


47-07 






45-60 






42-23 






40-69 






February, 


46-70 


46-69 




44-56 


44-66 




41-17 


41-45 




39-69 


40-19 




March, 


46-31 




46-42 


43-81 




46-16 


40-94 




45-80 


40-18 




45-58 


April, 


45-91 






43-75 






43-07 






43-54 






May, 


45-59 


45-69 




44-37 


44-38 




44-78 


44-85 




45-06 


45-61 




June, 


45-58 




46-40 


45-01 




46-12 


46-69 




45-97 


48-24 




45-82 


July, 


45-70 






46-52 






50-51 






52-69 






August, . 


46-07 


46-09 




47-99 


47-68 




51-61 


50-90 




52-67 


52-08 




September, 


46-51 




46-39 


48-54 




45-97 


50-59 




45*34 


50 89 




45-03 


October, . 


46-93 






48-52 






48-86 






47-85 






November, 


47-20 


47-12 




47-82 


47-75 




46-61 


46-68 




45-57 


45-40 




December, 


47-23 




46-29 


46-90 




45-73 


44-56 




45-24 


42-78 




45-03 


1895. 


























January, . 


47-05 






45-65 






40-91 






37-89 






February, 


46-72 


46-67 




44-01 


44-07 




37-84 


38-94 




35-49 


37-03 




March, . 


46"23 




46-2-2 


4256 




45-70 


38-07 




45-29 


37-71 




45-13 


April, 


45-59 






42-39 






40-96 






41-16 






May, 


45-17 


45-28 




43-25 


43-43 




44-59 


44-45 




45-81 


45-61 




June, 


45-07 




46-20 


44-65 




4570 


47-80 




4512 


49-85 




44-81 


July, 


45-29 






46-36 






50-33 






52-06 






August, . 


4576 


45-79 




47-67 


47-55 




51-25 


51-09 




52-71 


52-47 




September, 


46 33 




46-20 


48-63 




45-88 


51-70 




45-93 


52-63 




45-86 


October, . 


46-83 






48-86 






49-15 






47-49 






November, 


47-18 


47-08 




47-83 


47-76 




45-41 


45-99 




43-64 


44-12 




December,* 


47-22 




46-34 


46-60 




46-27 


43-42 




46-39 


41-24 




46-35 



OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 
Table II. — continued. 



173 





*i 


k 


h 


h 


Date. 


























1896. 


Monthly. 


Quarterly. 


Annual. 


Monthly. 


Quarterly. 


Annual. 


Monthly. 


Quarterly. 


Annual. 


Monthly. 


Quarterly. 


Annual. 


























January, . 


47-01 






45-35 






.42-09 






40-89 






February, 


4667 


46-66 




44-72 


44-80 




42-59 


42-20 




41-97 


41 -26 




March, . 


46-30 




46-52 


44-34 




46-47 


41-91 




46-46 


40-93 




46-34 


April, 


45-98 






44-12 






43-41 






43-90 






May, 


4577 


45-83 




44-71 


44-96 




46-16 


46-28 




47-61 


47-54 




June, 


45-75 




46-60 


46-06 




46-43 


49-28 




46-29 


51-12 




46-20 


July, . 


46-03 






47-46 






51-30 






53-03 






August, . 


46-47 


46-49 




48-55 


48-37 




51-67 


51-37 




52-67 


52-44 




September, 


46-97 




46-60 


49-09 




46-30 


51-14 




45-93 


51 61 




45-78 


October, . 


47-34 






48-86 






48-16 






46-45 






November, 


47 "55 


47-44 




47-55 


47-60 




44-76 


45-32 




43-12 


43-57 




December, 


47-42 




46-48 


46-39 




45-98 


43-04 




45-31 


41-15 




45-01 


1897. 


























January, . 


47-13 






45-29 






41-52 






39-43 






February, 


46-70 


46-65 




44-11 


44-27 




39-56 


40-74 




38-55 


39-55 




March, 


46-11 




46-26 


43-42 




4570 


41-14 




45-14 


40-68 




44-88 


April, 


45-60 






43-19 






41-14 






40-53 






May, 


45-26 


45-32 




43-39 


43-69 




43-55 


43-82 




44-47 


44-49 




June, 


45-09 




46-09 


44 50 




45-70 


46-77 




45-50 


48-47 




45-48 


July, . 


45-20 






45-78 






49-57 






51-79 






August, . 


45-57 


45-62 




47-48 


47-23 




51-99 


50-68 




53-79 


51-91 




September, 


46-08 




46-07 


48-42 




45-93 


50 48 




45-99 


50-16 




46-00 


October, . 


46-54 






48-25 






48-88 






48-45 






November, 


46-82 


4676 




47-72 


47-62 




47-22 


46-78 




46-76 


4599 




December, 


46-92 




46-21 


46-90 




46-16 


44-24 




46-26 


42-76 




46-28 


1898. 


























January, . 


46 82 






45-75 






43-47 






42-60 






February, 


46-55 


46-57 




45-30 


45-18 




42-87 


42 66 




41-67 


41-61 




Marcb, 


4634 




46-36 


44-49 




46-30 


41-63 




46-41 


40-55 




46-50 


April, 


4608 






44-11 






42-61 






42-60 






May, . 


45-83 


45-89 




44-50 


44*63 




44-70 


44-91 




45-21 


45-62 




June, 


45-75 




46-52 


45-27 




46-49 


47-41 




46-58 


49-04 




46-63 


My, 


45-85 






46 55 






50-22 






52-19 






August, . 


46-20 


46-23 




47-91 


47-77 




51-60 


51-29 




53-07 


52-78 




September, 


46-65 




46-65 


48-86 




46-51 


52-05 




46-39 


53-08 




46-37 


October, . 


47-12 






49-11 






50-32 






4992 






November, 


47*46 


47-39 




48-52 


48-38 




47-39 


47-44 




45-77 


46-52 




December, 


47-58 




46-69 


47-51 




46-44 


44-62 




46-28 


43-88 




46-35 


1899. 


























January, . 


47-42 






46-40 






43-12 






41-55 






February, 


47-11 


47-08 




45-06 


45-27 




41-24 


41-94 




39-76 


40-55 




March, 


4672 




46-73 


44-36 




46-56 


4147 




46-49 


40 33 




46-61 


April, 


46 35 






44-00 






41-78 






41-21 






May, . 


46-00 


46-06 




44-08 


44-36 




43-57 


44-46 




43-87 


45-56 




June, 


45-83 




4677 


45-01 




46-56 


48-04 




46-43 


51-61 




46-38 


July, 


45-95 






46-91 






51-00 






52-97 






August, . 


46-36 


46-38 




48-41 


48-23 




52-83 


52-11 




54-80 


53-81 




September, 


46-83 






49-38 






52-51 






53-66 






October, . 


47*36 






49-19 






49-16 






48-03 






November, 


47-64 


47-55 




48-37 


48-38 




47-24 


47-19 




46-09 


45 61 




December, 


47-65 






47-58 






45-16 






4271 







VOL. XL. PART I. (NO. 8). 



2 B 



174 MR THOMAS HEATH ON 



The Annual Curves. 



Complete tables of the whole of the observations made with the old set of rock 
thermometers during the forty years from 1837 to 1876 inclusive will be found in 
Volumes XL, XII., XIII. , and XIV. of the Edinburgh Astronomical Observations. 
This set of thermometers was erected at the Calton Hill in 1837 at the expense of the 
British Association for the Advancement of Science. At the same time two other sets 
were put up by the Association, one in the sandstone rock of Craigleith Quarry and 
another at the Experimental Gardens, now part of the Botanic Gardens. All three sets 
were established chiefly at the recommendation of the late Prof. J. D. Forbes. The 
two sets at Craigleith Quarry and at the Botanic Gardens were regularly observed for 
five years, and the results, along with those of the Calton Hill set for the same five 
years, are to be found in an interesting paper by Prof. Forbes, published in Vol. XVI. 
of the Transactions of the Royal Society of Edinburgh. The destruction of both these 
valuable sets of instruments appears to have taken place soon after the five years' 
observations had been secured. The Craigleith thermometers were maliciously destroyed 
in May 1842, and the set at the Experimental Gardens was broken by a storm in the 
winter of 1844-5. The sole remaining set, that in the rock of the Calton Hill, existed 
complete up to 1861, when t 2 , or the second deepest thermometer, was found broken off 
at the surface of the rock during the severe frost of the winter of 1860-61. The 
remaining three of this set were destroyed in September 1876 by an unfortunate 
Portuguese sailor, whom, on his arrest by the police, it was found necessary to place in a 
lunatic asylum. 

A complete description of the construction and erection of these thermometers, and 
a discussion of the method of determining the corrections of their readings, will be found 
in the paper by Prof. Forbes mentioned above, where he further discusses the results of 
the observations, and deduces the mean temperatures for the five years, the rate of 
increase of temperature with depth, and the ranges at different depths, showing how 
these depend on the varying conductivity of the strata at the three stations. The 
forms of the annual curves are then discussed, and their equations determined for each 
of the four thermometers at the three stations. The curves are shown graphically in a 
plate, and from these curves the epochs of maximum and minimum temperatures were 

obtained by interpolation. To obtain the value of the ratio /-, where k is the con- 
ductivity of the soil and c the specific heat, Prof. Forbes makes use of the equation 
log. A =A + Bp, where A is the therm ometric range at a depth p in French feet, A 
and B constants, of which B is always negative. The determination of these constants 
Prof. Forbes looked upon as the primary object of his investigation. A is equal to the 
logarithm of the thermometric range at the surface, or where p = 0. B determines the 
rate of diminution of the range below the surface, being smaller as the heat descends 
more readily, or as the conductivity is greater. This coefficient B was shown by 



OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 175 

Fourier to be equal to I™ log.e, where a = ./-. Hence, if A and B could be 

determined from the curves showing the range at different depths, and if c, the specific 
heat, were determined by laboratory experiment, the conductivity of the strata at the 
three stations could be deduced. Specimens of the three varieties of strata were 
submitted to M. Kegnault of Paris, who determined their specific heats by experiment, 
and from these values, combined with the values of B obtained from the curves, the 
values of k the conducting power of the strata were computed, "which," Prof. Forbes 
remarks, " has rarely been so accurately determined for any form of matter." 

This research of Prof. Forbes has a special interest, to which no later investigation 
of the rock thermometer observations in Edinburgh can aspire, inasmuch as the 
existence of the three sets enabled him to compare the different circumstances depend- 
ing on the locality of the instruments, more particularly the relative conducting powers 
of the different rocks or soils in which they were buried. The destruction of two of the 
sets prevents any redetermination of these quantities by this method from a longer 
series of observations so far as these two stations are concerned, and the loss at a later 
date of t 2 at Calton Hill still further restricted the material for investigation. After 
the Calton Hill set. however, had been in existence for a further period of thirteen 
years, Lord Kelvin (then Prof. William Thomson) and Prof. Everett, in papers read 
before the Koyal Society of Edinburgh on the 30th April 1860, re-discussed the whole 
of the physical phenomena concerned, both from the theoretical and practical points of 
view. Lord Kelvin, specially, shows how the theory of periodic variations can be 
applied to the particular case of terrestrial temperature. As Prof. Forbes had already 
done, he adopts Fourier's solution of the problem, and applies it in a more elaborate 
form than Prof. Forbes had attempted. Fourier's solution of the problem of the 
deduction of the conductivity of the strata from the retardation of epoch, and the 
amplitude at different depths, may be stated in Lord Kelvin's own words : "If the 
temperature at any point of an infinite plane, in a solid extending infinitely in all 
directions, be subjected to a simple harmonic variation, the temperature throughout the 
solid on each side of the plane will follow everywhere according to the simple harmonic 
law, with epochs retarded equally, and with amplitudes diminished in a constant pro- 
portion for equal augmentations of distance. The retardation of epoch expressed in 
circular measure (arc divided by radius) is equal to the diminution of the Napierian 
logarithm of the amplitude ; and the amount of each per unit of distance is equal to 

/ ,, if c denote the capacity for heat of a unit bulk of the substance, and k its 

conductivity. 

" Hence if the complex harmonic functions expressing the varying temperature at 
two different depths be determined, and each term of the first be compared with the 

corresponding term of the second, the value of ~ may be determined either by 



176 MR THOMAS HEATH ON 

dividing the difference of the Napierian logarithms of the amplitudes, or the difference 
of the epochs by the distance between the points. The comparison of each term in the 
one series with the corresponding term in the other gives us, therefore, two determina- 
tions of the value of / j~, which should agree perfectly, if (l) the data were perfectly 

accurate, if (2) the isothermal surfaces throughout were parallel planes, and if (3) the 
specific heat and conductivity of the soil were everywhere and always constant." 

By the method thus indicated Lord Kelvin applied the general theory — 1st, to the 
five years' observations at the three stations ; 2nd, to the thirteen years' observations 
at Calton Hill alone. The result he brought out was that the figures representing the 

conducting power of the rock at Calton Hill, the values of / -,-, as deduced from the 

diminution of amplitude, and from the retardation of epoch, appear to diminish as the 
deeper thermometers are approached. There are thus outstanding discrepancies from 
Fourier's theory, which supposes that the values should come out alike for all depths. 
Lord Kelvin states his opinion that " there can be no doubt but that this discrepance 
is not attributable to errors of observation, and it must therefore be owing to deviation 
in the natural circumstances from those assumed for the foundation of the mathematical 
formula." Later on he says : " I can only infer that the residual discrepancies .... 
are not with any probability attributable to variation of conductivity and specific heat 
in the rock, and conclude that they are to be explained by irregularities, physical and 
formal, on the surface." Some of these irregularities he specifies, the ground rising 
slightty to the east and falling abruptly at a distance of about 15 yards on the west, the 
immediate surface being flat, partly covered with grass, partly with gravel. 

It thus appeared to be of great interest to see whether the reduction of the whole 
series of forty years' observations of the old thermometers, and the series of twenty years 
of the new thermometers erected in 1879 would bring out a similar or a more satis- 
factory result. In carrying out this work I have availed myself largely of the elegant 
methods of procedure detailed in the paper by Prof. Everett mentioned already. The 
readings of the thermometers have throughout been made once a week, on Mondays at 
noon, and the corrected readings for 1837-76, which were published in the Edinburgh 
Astronomical Observations, have now been taken out and arranged in four series of ten 
years, under each Monday of the year. The means of the columns so formed give the 
temperature of each thermometer for the mean date of the Monday to which it belongs. 
The average of the four series of ten years were then taken as the final temperatures 
from which the annual curves of the old set of thermometers were obtained. 

In computing the equations of these curves, or the harmonic function of the 
temperature at any time represented by the fraction of the year, I have followed Prof. 
Everett in dividing the year into twelve parts instead of thirty-two, the division Lord 
Kelvin adopted. I have done so for two reasons — (1) because the labour involved is 
much less, the equations being solved by a simple method of elimination, and the 



OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 



177 



accuracy attainable is sufficient for the purpose ; (2) because the fifty-two weekly mean 
temperatures could be divided up into twelve lots, eight of four each, and four of five 
each, the means of which would not differ much in weight, and these monthly means 
could be used in solving the equations, without having to resort to the necessity of 
interpolating values from the curves themselves, a method which is not so accurate, 
unless the curves are drawn on a very large scale. The year was then divided into 
twelve equal parts, starting from the mean date of the first Mod day. This date for the 

365'25 

forty years is January 4"10. If to this we add __ = 30*4375 days, and consider 

February as consisting of 28 "25 days, we arrive at the following twelve equi-mensual 

dates. 

4-10 July, . . . 5-48 



February, . 


. 3-54 


March, 


. 5-72 


April, 


. 5-16 


May, 


. 5-60 


June, 


. 5-04 



August, 


. 4-93 


September, 


. 4-35 


October, 


. 4-79 


November, 


. 4-22 


December, 


. 4-66 



As, however, the mean dates of the four or five weekly mean temperatures used in 
forming the twelve monthly means did not generally come out quite the same as the 
equi-mensual dates, it was necessary to apply a small correction depending on the rate 
of increase or decrease of temperature at the time. This correction is always small, its 
greatest values being +0 C, 015 in the case of t x and -f-0°"208 for t 4 . The following table 
gives the monthly mean temperatures thus deduced, and their dates for the old 
thermometers from forty years' observations, except in the case of t 2 , of which only 
twenty-four years' observations had been secured at the date of its fracture. 

OLD THERMOMETERS. 



Equi-mensual Date. 


'i 


h 


h 


h 






°F. 


°F. 


°F. 


°F. 


January, 


4-10 


47-876 


47-358 


44-324 


41-346 


February, 


3-54 


47-789 


46-297 


42-876 


40-150 


March, 


5-72 


47-572 


45-386 


42-169 


40-003 


April, . 


5J6 


47-275 


44-811 


42-382 


41-407 


May, . 


5-60 


46-975 


44-737 


43-868 


44-535 


June, . 


5-04 


46-736 


45-275 


46-214 


48-462 


July, . 


5-48 


46-629 


46-376 


49-007 


52-164 


August, 


4-93 


46-690 


47-672 


51-073 


53-945 


September, . 


4-35 


46-922 


48-756 


51-701 


53-416 


October, 


4-79 


47-256 


49-292 


50-858 


50-829 


November, . 


4-22 


47-582 


49-163 


48-800 


46-789 


December, . 


4-66 


47-813 


48-412 


46-168 


43-330 


T„ = 


47-2596 


46-9612 


46-6200 


46-3647 



178 



MR THOMAS HEATH ON 



The new thermometers were similarty treated for the twenty years' observation avail- 
able at the end of 1899. It is a somewhat unfortunate circumstance, however, that 
there exists no record of the relative capacity of the different parts of the tube of which 
these new thermometers are made, so far as could be discovered after enquiry. This 
appears to be due to the lamented deaths of Mr Richard Adie, the head of the firm 
of Messrs Adie & Sons, and of Mr Thomas Wedderburn, who was their responsible 
manager when they held the contract for the construction of the thermometers. It is 
known, however, that the new instruments were made with, as nearly as possible, the 
same size of tube as the old ones. We may therefore be considered justified in 
supposing that the relative capacities of the capillary parts and the wide parts of 
the tubes are, approximately, the same in the new set as they were in the old, 
and that the only difference of importance is to be found in the different lengths 
of the two sets. By far the greater part of the total corrections applied to the old 
readings was that depending on the difference of temperature of the bulb and of the 
wide part of the tube above ground, or the correction for the temperature of the air, 
and only a small part, never more than 0*03 of a degree F. for the longest thermometer, 
was due to the temperature of the stem. The corrections to be applied to the 
new set may then without risk of important error be assumed the same as those of 
the old. 

The following table gives the values of the monthly mean temperatures and the 
equi-mensual dates for the new thermometers from the twenty years' readings, 1880-1899. 



NEW THERMOMETERS. 



Equi-meusual Dates. 


h 


h 


*3 


U 






°F. 


°F. 


°F. 


°F. 


January, 


3-95 


47-097 


45-788 


42-082 


40-128 


February, 


3-39 


46-767 


44-597 


40-949 


39-465 


March, 


5-57 


46-343 


43-780 


40-534 


39-421 


April, . 


5-01 


45-920 


43-314 


41-154 


40-748 


May, . 


5-45 


45-553 


43-470 


43-211 


43-853 


June, . 


4-89 


45-352 


44-395 


46-382 


48-045 


July, . 


5-32 


45-405 


45-873 


49-545 


51-638 


August, 


4-77 


45-716 


47-341 


51-170 


52-815 


September, . 


4-20 


46-198 


48-358 


51-158 


52-295 


October, 


4-64 


46-700 


48-681 


49-815 


49-387 


November, . 


. 4-08 


47-088 


48-149 


46-963 


45-541 


December, . 


4-51 


47-238 


47-273 


44-386 


42-477 


T = 


46-2814 


45-9182 


45-6124 


45-4844 



From the numbers in this table the equations to the curves for the new thermometers 
have been formed. 

In the reduction of the readings of the new thermometers, the corrections have 
not been applied to the single readings, nor to the monthly, quarterly, and annual means 



OBSERVATIONS OF THE EDINBURGH BOCK THERMOMETERS. 179 

deduced from them (Tables I. and II.). They have, however, been applied to the 
weekly averages of twenty years used in the graphical drawing of the annual curves. 
The corrections used for this purpose are the means of the corrections applied to the 
old thermometers in the corresponding weeks over the ten years, 1837-46. The 
similarity between the two sets of curves would seem to afford a sufficient assurance 
that the corrections thus applied can be only inappreciably in error, allowance being 
of course made, in comparing two curves, for the fact that the length of the longest 
of the new tubes is only 250 inches, while that of the longest old one was 307 inches, 
the other new tubes being also shorter than the corresponding ones of the old set. 
This difference of length has, as has been said, but slight effect on the amount of the 
correction to the readings, only about a maximum of 0"006 of a degree F. It has 
however, a considerable influence on the form of the curve. As might have been 
anticipated, a glance at Plates II. and III. will show, that in the new set the annual range, 
is greater than in the old, but the retardation of epoch is less. While, then, it is to 
be regretted that the corrections of the new thermometers cannot be determined with 
the same order of accuracy and confidence with which those of the old set were worked 
out by Prof. Forbes (Vol. XVI., Transactions, Royal Society, Edinburgh), it is reassuring 
to be able to say, in the words of the late Prof. Piazzi Smyth, that " although these 
new thermometers cannot compete with the old ones as instruments of the most 
delicate Natural Philosophy chamber problems, I have been much pleased to find 
that, step by step, they have shown their full sufficiency to keep up the differential 
historical record of superannual cycles of temperatures." 

Having already no less than forty years' observations of the old set, with a complete 
theory of their corrections, rigorously applied to each individual reading, and having 
worked out the forms and the equations of the annual curves, and deduced therefrom 
the conductivity of the rock, it would appear to be almost superfluous to attempt to 
derive the same quantities from the twenty years' readings of the new set, when the 
result, owing to the difficulty involved in the corrections, must necessarily be somewhat 
less reliable. It was thought that this part of the work should be undertaken, however, 
in the hope that a comparison of the results would form a more or less crucial test of 
the propriety of the corrections which have been applied, and of the value of the new 
set for carrying on the " historical record " alluded to by Prof. Piazzi Smyth. The value 
of the conductivity of the soil can be derived either from the difference of the Napierian 
logarithms of the amplitude at different depths, or from the difference of the epochs. Now 
the corrections take the positive sign in the winter months and the negative sign in the 
summer. Hence in the case of the deepest thermometers in each set, which have their 
highest readings in winter and their lowest in summer, the range is increased ; whereas, 
with the other three of each set the range is more or less diminished by the application 
of the corrections. But the epochs are not similarly affected, because the corrections 
follow a very smooth curve. Hence, if the two determinations of the conductivity by 
means of the new thermometers agree fairly well with one another, and with the 



180 



MR THOMAS HEATH ON 



similar determinations by means of the old set, we may reasonably conclude that the 
corrections have not been appreciably erroneous, and that the new thermometers may 
be confidently accepted as fairly competent to take the place of the old ones, allowance 
being made for the difference of the depths of the two sets. 



Equations to the Curves. 

We may put the equation to the curve in the form 

T = T + a 1 sin(27r/+?- 1 ) + a 2 sin(47r/ + ?- 2 ) + &c. 
where T is the mean temperature of the year, a x and a 2 ^ ne half- amplitude of the 
annual and semi-annual terms respectively, f the fraction of the year, and 7\ and r 2 the 
retardation of phase of the same two terms. If we put c^ = a x sin r v and /5 X = <x x cos r 1? 

Ct 

then s/( a l + PI) = a i an d nr = ta,nr 1 . Substituting these values of a x and r v and 
similar values of a 2 and r 2 , we reduce the equation to the form 

T = T + (a 1 COs27r/ + /3 1 sin27r/) + (a 2 cos47r/'+^ 2 siii47r/) + &c. 

Giving to f the successive values 0, ■£%, T 2 2, \^, we form the following 

twelve equations : — 

T-T = +a 1 +a 2 

= + a x cos 30° + ft sin 30° + a 2 cos 60° + ft sin 60° 

= + a x cos 60° + ft sin 60° - a 2 cos 60° + ft sin 60° 

= + ft -a 2 

= - a x cos 60° + ft sin 60° - a 2 cos 60° - (3 2 sin 60° 

= - dj cos 30° + ^ x sin 30° + a 2 cos 60° - /3 2 sin 60° 

= -a x +a 2 

= - a x cos 30° - ft} sin 30° + a 2 cos 60° + /3 2 sin 60° 

= - a x cos 60° - (3 1 sin 60° - a 2 cos 60° + /3. 2 sin 60° 

= -ft -a 2 

= + a x cos 60° - (3 1 sin 60° - a 2 cos 60° - /?., sin 60° 

= + a 1 cos 30° - ft sin 30° + a 2 cos 60° - ft sin 60° 

The eight sets of values of T — T are contained in the two tables on pp. 177 and 178 
for the old and new thermometers respectively. In working out the equations, Prof. 
Everett's method of elimination has been followed, and the results are shown in the 
following tables : — 







Old. 






New. 




*1 


h 


3 


h 


h 


h 


h 


h 


a l 

fit 


+ 0-6265 
+ 0-0112 
-0-0063 
-00193 


+ 0-5060 
- 2-2480 
-00938 
+ 0-0757 


-2-3535 
-4-1797 
-0-0022 
+ 0-3996 


- 5-4648 

- 4-5537 
+ 0-3077 
+ 0-6347 


+ 0-8458 
-0-4003 
-0-0288 
-0-0298 


+ 00135 
-2-6992 
-0-0682 
+ 01 140 


-3-5798 
-4-2038 
+ 0-1947 
+ 0-4140 


-5-5810 
-4-1902 
+ 0-4128 
+ 0-5890 



OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 



181 



From these values of a l9 ft v a 2 , and /3 2 , the corresponding values of a x , r x , a 2 , and r^ 
were deduced. 







Old. 






New. 




*1 


h 


h 




h 


k 


h 


h 


a. 2 

»*2 


0-627 
88°-58'-6 
0-020 
198°-4'-6 


2-304 
167°-18'-9 

0-120 
308°-54'-2 


4-796 
209°-23'-0 

0-400 
359°-42'-0 


7-113 

230°-ll'-8 
0-705 
25°-51'-8 


0-936 
115°-18'-6 

0-041 
224°-l'-3 


2-699 
179°-42'-3 

0-133 
329°-6'-5 


5-522 
220°-25'-0 
0-458 
25°-ll'-0 


6-979 

233°-6'-0 

0-719 

35°-l'-5 



Substituting these values in the original general equation, we have the following 
eight equations to the annual curves for the two sets of thermometers. 



i old t x 


T = 


47°- 


old t 2 


T = 


46 • 


old t 3 


T = 


46 • 


old t 4 


T = 


46 • 


new t 1 


T = 


46 -. 


new t, 2 


T = 


45 • 


new t 3 


T = 


45 • 


new t 4 


T = 


45 • 



260 + 0-627 sin (2tt/+ 88°-58'-6) + 0"020 s 
961 + 2-304 sin (2tt/+ 167 '18 -9) + 0-120 s: 
620 + 4-796 sin (2tt/+ 209 -23 -0) + 0-400 s 
365 + 7-113 sin (2tt/+ 230 -11 -8) + 0-705s 
281 + 0-936 sin (2ir/+ 115 -18 -6) + 0-041 s 
918 + 2-699 sin (2tt/+ 179 -42 -3) + 0-133 s 
612 + 5-522 sin (2tt/+ 220 -25 -0) + 0-458 s 
484 + 6-979 sin (2tt/+ 233 ■ 6 -0) + 0719 s 



n(47r/+198 c 
n(47r/+308 c 
n(47r/+359 e 
n(47r/+ 25 c 
n(47r/+224 c 
n(47r/+329 
n(4«/+ 25 
n(47r/+ 35 



4' 
54' 
42' 
51' 

r 

6 

ii 
i 



•6) + &c. 
•3)+&c. 
■0) + &c. 
•8) + &c. 
•3) + &c. 
•5) + &c. 
•0) + &c. 
•5) + &c. 



The maximum and minimum values of the annual and semi-annual terms in these 
equations will be found by making the various sines successively equal to + 1 and — 1, 
or the angles concerned equal to ±90°. The values of f, the fraction of the year 
(reckoning from the mean date of the first Monday) corresponding to the maximum 
and minimum values of the several terms, were deduced from the equations so formed. 
The following is a synopsis of the eight thermometers arranged in order of depth, 
showing the amplitudes and dates of maxima and minima of the annual and semi- 
annual terms respectively. 

ANNUAL TERM. 







Feet. 


Semi- 
Amplitude. 


Dates of 




Maximum. 


Minimum. 


Old t x . 
New t l . 
Old t. 2 . 
New t 2 . 
Old t s . 
New ^ . 
Old t A . 
New t t . 




25-6 

21-0 

12-8 

11-1 

6-4 

5-0 

3-2 

3-1 


0-627 
0-936 
2-304 
2-699 
4-796 
5-522 
7-113 
6-979 


January 5'1 
December 9'5 
October 17 "9 
October 5 "2 
September 5 '2 
August 24-9 
August 15 "1 
August 12'0 


July 6-7 
June 9-9 
April 18-3 
April 5-6 
March 6-6 
February 23'3 
February 13 - 5 
February 10'4 



VOL. XL. PART I. (NO. 8). 



2 C 



182 



MR THOMAS HEATH ON 



SEMI-ANNUAL TERM. 







Feet. 


Semi- 
Amplitude. 


Dates of 




Maxima. 


Minima. 


Old *, . 

New t x . 
Old t 2 . 
New t~ 2 . 
Old t 3 . 
New t 3 . 
Old t 4 . 
New t i . 




25-6 

21-0 

12-8 

11-1 

6-4 

5-0 

3-2 

31 


0-020 
0-041 
0-120 
0-133 
0-400 
0-458 
0-705 
0-719 


May 11-9, November 10 '5 
April 28-6, October 28"2 
March 16-7, September 15"3 
March 6-3, September 4"9 
February 18-9, August 20"5 
February 5 - 8, August 7 "4 
February 5 - 7, August 7 '3 
February - 8, August 2*5 


February 9-6, August 11 3 
January 27 -3, July 28'9 
December 15'6, June 16'0 
December 5 - 2, June 5 - 6 
November 19-9, May 21 '2 
November 6 "7, May 8'1 
November 6-6, May 8-0 
November T7, May 3'2 



We are now in a position to deduce the conducting power of the rock, both from 
the Napierian logarithms of the amplitudes, and from the retardation of phase, expressed 

/7TC 

in circular measure. We have the two values of /^= Alog e a= Ar, where T is 

the period, one year for the annual term, and half a year for the semi-annual. 

The following table gives the values of r x and r 2 in circular measure, and the 
Napierian logarithms of a x and a 2 . 





Depth. 


r i 


V 2 


Log, fflj 


Log, a 2 




Feet. 










Old t x 


25-6 


1-553 


3-457 


-0-467 


-3912 


h 








12-8 


2-920 


5-391 


+ 0-835 


-2-120 


h 








C-4 


3-654 


6-278 


+ 1-568 


-0-916 


h 








3-2 


4018 


6-735 


+ 1-962 


-0-350 


New tj 








21-0 


2-013 


3910 


-0-066 


-3-194 


h 








111 


3-136 


5-744 


+ 0-993 


-2-017 


h 








5-0 


3-847 


6-723 


+ 1-709 


-0-781 


h 








31 


4-068 


6-894 


+ 1-943 


-0-329 



If we now take every possible combination of two thermometers from the four in 
each set, and divide the differences of their retardations of phase, and of the logarithms of 
their amplitudes, by the difference of depth in feet, we get the following two tables 



7TC 



showing the values of K f -j- for the annual and the semi-annual terms. 



OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 



183 



VALUES OF J 1 ^- FROM THE ANNUAL TERM. 





Diff. of 
Depth. 


Ar, 


/■7TC 


A log, a x 




Old. 


Feet. 










t x and t 2 


12-8 


1-367 


0-107 


1-302 


0-102 


t 1 and t 3 


19-2 


2-101 


0-109 


2-035 


0-106 


t 1 and t i 


22-4 


2-465 


0-110 


2-429 


0-108 


t 2 and t 3 


6-4 


0-734 


0-115 


0-733 


0-115 


t 2 and t i 


9-6 


1-098 


0-114 


1-127 


0-117 


t 3 and t 4 


3-2 


0-364 


0-114 


0-394 


0-123 






Mean 


0-1115 


Mean 


0-1118 


New. 












t-y and t 2 


9-9 


1-123 


0-113 


1-059 


0-103 


t x and t 3 


16-0 


1-834 


0-115 


1-775 


0-111 


t x and t 4 


17-9 


2-055 


0-115 


2-009 


0-112 


t and t 3 . . . 


6-1 


0-711 


0-117 


0-716 


0-117 


£ and £ 4 


8-0 


0-932 


0-116 


0-950 


0-119 


i 3 and t 4 


1-9 


0-221 


0-116 


0-234 


0-123 






Mean 


0-1153 


Mean 


0.1148 



VALUES OF 



lire 



FROM THE SEMI-ANNUAL TERM. 





Diff. of 
Depths. 


Ar, 


^ 


vf 


A log, a 2 


^ 


lire 


Old. 


Feet. 














t x and t 2 


12-8 


1-934 


0-151 


0-107 


1-792 


0-140 


0-099 


t x and t 3 


19-2 


2-821 


0-146 


0-103 


2-996 


0-156 


0-110 


t x and £ 4 


22-4 


3-278 


0-146 


0-103 


3-562 


0-159 


0-112 


t 2 and t 3 


6-4 


0-887 


0-139 


0-098 


1-204 


0-188 


0133 


t. 2 and t i 


9-6 


1-344 


0-140 


0-099 


1-770 


0-184 


0-130 


t 3 and t± 


3 2 


0-457 


0-143 


0-101 


0-566 


0-177 


0-125 








Mean 


0-1018 




Mean 


0-1182 


New. 
















t x and t 2 


9-9 


1-834 


0-185 


0-131 


1-177 


0-119 


0-084 


t x and t 3 


16-0 


2-813 


0-176 


0-124 


2-413 


0-151 


0-107 


t x and ^ 4 . . . 


17-9 


2-984 


0-167 


0-118 


2 865 


0-160 


0-113 


t 2 and £ 3 . . . 


6-1 


0-979 


0-160 


0-113 


1-236 


0-203 


0-144 


< 2 and t i 


8-0 


1-150 


0-144 


0-102 


1-688 


0-211 


0-149 


t 3 and £ 4 


1-9 


0-171 


0090 


0-064 


0-452 


0-238 


0-168 








Mean 


0-1087 




Mean 


0-1275 



184 



MR THOMAS HEATH ON 



The values of 



J-rrC 

VI 



deduced from the epoch and amplitude of the annual term 



agree amongst themselves much better than the values derived from the semi-annual 
term. In the case of the latter, however, the coefficients are so small that any better 
agreement could hardly be expected. It will be seen from these tables that all the 
four mean values derived from the new thermometers are somewhat greater than those 
from the old, and that the two values from the old and new derived from the 
amplitudes of the semi-annual term are both greater, and by nearly the same amount, 
than those derived from the retardation of phase. The results from the annual term 
specially show also a distinct tendency to decrease as the deeper thermometers are 
approached, a tendency which was pointed out by Lord Kelvin in his paper referred to. 
This will be more clearly seen from the following table, showing the results from both 
sets of thermometers and from both the terms of the equations, arranged in the order 
of the means of the depths of the two thermometers concerned in each case. 



VALUES OF 



/ttC 

VT 



IN OEDEE OF MEAN DEPTH. 











Mean 
Depth. 


Annual Term. 


Semi-Annual Term. 








From 
Phase. 


From 
Amplitude. 


From 
Phase. 


From 
Amplitude. 


Means. 


Old t x and t 2 
Old t x and t 3 
New t x and t 2 
Old t x and t 4 
New tj and t 3 
New t l and t 4 
Old t 2 and t 3 
Old t 2 and i 4 
New t 2 and t 3 
New t 2 and t 4 
Old t z and t 4 
New t 3 and t 4 








19-2 

16-0 

16-0 

14-4 

13-0 

12-0 

9-6 

8-0 

8-0 

7-1 

4-8 

4-0 





107 
109 
113 
110 
115 
115 
115 
114 
117 
116 
114 
116 





102 
106 
107 
108 
111 
112 
115 
117 
117 
119 
123 
123 





107 
103 
131 

103 
124 
118 
098 
099 
113 
102 
101 
064 





099 
110 
084 
112 
107 
113 
133 
130 
144 
149 
125 
168 





104 
107 
109 
108 
114 
115 
115 
115 
123 
121 
116 
118 



The tendency of the value of / — to decrease with increasing depth is very apparent 

from about 7 feet deep, to the lowest depths in question. The shorter thermometers 
of each set, however, show strange irregularities, which seem difficult to explain, 
except on the supposition that owing to surface conditions different from those assumed 
as the foundation of the harmonic law, they do not follow that law with so great a 
degree of exactness as the deeper ones. In the case of the results from new t 3 and t A , 
some part of the irregularities may also be due to the sinking of these thermometers, 
to which I have already referred, since their establishment in the rock. The general 
tendency of the deeper thermometers to give smaller values is, however, apparent, and 
seems to suggest that the conducting power of the rock increases with depth. 



OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 



185 



From these values of 



lire 

V "P 



k 
the value of -, the conductivity of the rock expressed 



" in terms of the thermal capacity of a cubic foot of its own substance " can now be 
deduced, and finally the value of k, the conductivity expressed in terms of the thermal 
capacity of a cubic foot of water. In the following table these are compared with the 
values deduced by Prof. Forbes, Lord Kelvin, and Prof. Everett. As the earlier com- 
putations have been all referred to the French foot as the unit of measure, it has been 
necessary to reduce them to the English foot.* The value of c, the specific heat of the 
rock per unit of volume used, is 0'5283, the number determined by M. Regnault at 
Prof. Forbes' request. 





firC 

V F 


k 
c 


k 


Per 

French Foot. 


Per 

English Foot. 


Per 
French Foot. 


Per 
English Foot. 


Per 

French Foot. 


l 

Per 

English Foot. ; 


Prof. Forbes, 
Lord Kelvin, 
Prof. Everett, 
Old Thermometers, 
New Thermometers, 


0-1152 
0-1156 
0-1174 


0-1116 

0-1150 


(236-7) 

2351 

(227-9) 


267-0 

252-2 
237-5 


(125-0) 
(124-2) 
(120-4) 


142-0 
141-1 
(136-8) 
133-2 
125-7 



The numbers enclosed in brackets are not given in the papers of the authors opposite 
whose names they are placed. 

From the dates of the maxima and minima of the various thermometers we can 
determine the time necessary for heat to pass through 1 foot of the rock of Calton Hill. 





Mean Depth. 
Feet. 


Days. 


From old t x and t 2 . 


19-2 


6-2 


new t x and t 2 . 


16-0 


6-6 


old t 2 and t 3 . 


9-6 


6-7 


new t 2 and i s . 


8-0 


6-8 


old t s and t i . 


4-8 


6-6 


new t 3 and t i . 


4-0 


6-8 J 



>- 6 - 6 days. 



To determine the mean annual range at different depths, 1 have plotted the curve, 
Plate IV., showing the ranges taken from the equations to the annual curves. Accord- 
ing to theory the range decreases geometrically as the depth increases in arithmetical 
progression, or the curve is a logarithmic curve. Hence we have log. R = A + Bp, where 
R is the range at a depth p in feet, A is evidently the logarithm of the range at the 
surface, where p = and B is a constant fixing the rate of decrease of the range below 
the surface. This surface range I have taken = 20°, or the mean value shown by the 
curves. Hence log. 20 = A= 1 "30103. From the point on the curve where the range 

* French foot = English foot x 1-06575 ; (l-06575) 2 = 1-13582. 

VOL. XL. PART I. (NO. 8). 2 D 



186 MR HEATH ON OBSERVATIONS OF THE EDINBURGH ROCK THERMOMETERS. 



is 10°, we have 1=A + Bp 10 , and p 10 = 6*2 feet. From these equations we find B 
-0-0485. 
Again p lt the depth where the range is 1° F. = — ^ =26'8 feet. 

Similarly p^ = - — ^ — =* 47 "4 feet. 



p-< 



B 

2+A 
B 



= 68-1 feet. 



Rainfall and Mean Shade Temperature from Scottish Meteorological Society's 
Returns, published in the Registrar General's Quarterly Reports. 







1888. 


1889. 


1890. 


1891. 


1892. 


1893. 




Rain. 


Mean 
Temp. 


Rain. 


Mean 
Temp. 


Rain. 


Mean 
Temp. 


Rain. 


Mean 
Temp. 


Rain. 


Mean 
Temp. 


Rain. 


Mean 
Temp. 


Januan 

Februai 

March, 

April, 

May, 

June, 

July, 

August, 

Septem 

October 

Noverol 

Decemb 


h '■ 
7> ■ 

aer, . 

>er, . 
er, . 


2-97 
1-61 

339 
2-14 
2-84 
2-54 
4-69 
2-66 
1-34 
2-91 
6-23 
3-33 


38-5 
35-3 
357 
424 

48-3 
52-0 
53-7 
54-5 
51-7 
46-8 
42-9 
40-5 


2-55 

2-92 
2-32 
3-01 
2-24 
0-99 
2-82 
5-40 
1-70 
3-99 
2-11 
3-39 


39-5 
36-8 
39-6 
42-8 
53-1 
57-1 
55-9 
55-9 
524 
45-6 
434 
39-0 


5-80 
1-08 
3-38 
1-44 
2-19 
3-96 
3-79 
3-90 
3-84 
4-45 
6-77 
1-67 


41-0 
37-8 
41-6 
43-6 
51-0 
53-9 
54-7 
55-2 
56-4 
48-4 
41-0 
352 


2-67 
1-26 
3-35 
1-20 

2-28 
1-14 
2-87 
551 
5-16 
4-31 
3-72 
5-80 


36-1 
41-6 
37-0 
41-3 

46-8 
55-6 
57-3 
55-6 
54-3 
46-7 
40-5 
38-5 


3-42 
2-44 
1-15 
1-22 
3 65 
3-11 
2-56 
5-34 
401 
4-69 
3-41 
1-98 


35-8 

36-8 
363 
43-2 
49-2 
52-8 
54-8 
55-6 
50-2 
42-8 
42-1 
34-0 


2-22 
4-01 
1-54 
1-40 
1-88 
2-12 
3-35 
3-56 
3-45 
4-51 
3-66 
4-67 


36-3 
38-3 

42-7 
47-2 
52-4 
57-0 
576 
59-4 
518 
47 
39-5 
40-5 






36-65 


45-2 


33-44 


46-7 


42-27 


46-6 


39-27 


45-9 


36-98 


44-5 


36-37 


47-5 



January, 


1894. 


1895. 


1896. 


1897. 


1898. 


1899. 


Rain. 


Mean 
Temp. 


Rain. 


Mean 
Temp. 


Rain. 


Mean 
Temp. 


Rain. 


Mean 
Temp. 


Rain. 


Mean 
Temp. 


Rain. 


Mean 
Temp. 

36-6 


4-85 


36-6 


2-76 


30-8 


2-53 


39-7 


1-75 


34-2 


3-14 


42-9 


5-02 


February, 


7-05 


38-6 


1-17 


29-0 


2-00 


41-4 


2-84 


39-4 


3-90 


38-2 


2-69 


38-5 


March, . 


2-73 


42-4 


3-55 


39-6 


4-12 


41-2 


4-89 


40-4 


2-27 


39-6 


3-44 


40-2 


April, . 


1-43 


47-1 


2-16 


45-1 


2-03 


47-0 


2-17 


41-9 


3-61 


45-6 


3-87 


43-0 


May, . 


3-46 


45-2 


0-90 


51-8 


0-98 


53-0 


2-29 


47-3 


2-62 


47-7 


3-29 


46-3 


June, . 


2-50 


535 


2-14 


55-0 


3-39 


56-2 


4-10 


54-3 


2-32 


54-4 


1-80 


57-4 


July, . 


3-64 


58-2 


4-37 


55-5 


3-89 


56-6 


2-44 


58-2 


1-52 


56-5 


3-46 


59-1 


August, 


4-78 


55-1 


5-22 


57-8 


2-75 


55-0 


4-59 


58-9 


4-36 


57-3 


1-34 


60-1 


September, . 


0-53 


51-2 


1-75 


57-2 


4-87 


52-4 


3-46 


51-0 


373 


56-0 


4-59 


51-9 


October, 


3-34 


45-2 


4-61 


42-8 


4-62 


42-2 


2-47 


48-0 


4-42 


50-1 


3-10 


47-8 


November, . 


3-63 


443 


4-44 


41-8 


1-90 


41-5 


3-24 


44-6 


5-05 


41-7 


4-85 


464 


December, . 


3-84 


39-6 


4-38 


37-4 


5-61 


37-6 


5-37 


38-6 


6-07 


42-6 


4-16 


35-6 


41-78 


46-4 


37-45 


45-3 


38-69 


47-0 


39-61 


46-4 


43-01 


47-7 


41-61 


46-9 






Trans Ro\ Soc Edin 






ROYAL OBSERVATORY, EDINBURGH. ROCK THERMOMETERS. 

Compared with the Sun-Spot Curve, Scottish Air Temperature and Rainfall. 

Quadruple Annual Means of Temperatures from I88O to 1899, Cleared from the Effects of Annual Range. 



PLATE I. 




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> 



- 






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Vol XL. 



EDINBURGH ROCK THERMOMETERS. ANNUAL CURVES. 

Old t t and t 2 , and New ti and t 2 . 



PL A TE 2. 



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New tj 20.9 feet deep. 

t 2 11.1 „ 

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Be. Edin. Vol. XL. 

EDINBURGH ROCK THERMOMETERS. ANNUAL CURVES. 

Old t 3 and t 4 , and New t 3 and t 4 . PLATES. 




« ft A : 

ft /> I U ' ■ 



sWj'AL H'. 



Edin. 



EDINBURGH ROCK THERMOMETERS. 
RANGE AT DIFFERENT DEPTHS. 



Vol. XL. 



















PLA TE 


4. 




RANGE. 


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( 187 ) 



IX. — Some Identities connected with Alternants, and with Elliptic Functions. 

By Thomas Muir, LL.D. 

(Read December 3, 1900.) 

(1) Cayley in his paper* entitled "Note sur l'addition des fonctions elliptiques" 
obtains among other similar things an expression for 



in terms of 
where 



S(u + v -f- w . . . ) 
Su, Sv, Sw, . . . 



Su = Jk • sinam —pr 



The form of the expression is the quotient of two determinants, and as the expression 
becomes useless for such cases as u = v, u = w, . . . on account of the simultaneous 
vanishing of numerator and denominator, he is led to seek a means of throwing out the 
common evanescent factors. In doing so there is brought to light the need for the 
existence of certain identities, viz., 

in connection with the numerator and denominator for the case of three arcs the 
respective identities 



1 


a A 


1 


b B 


1 


c C 


1 


a aA 


1 


b 6B 


1 


c cC 



(B + C)(C + A)(A + B) = 



(B + C)(C + A)(A + B) = 



1 


a 


A 2 


1 


b 


B 2 


1 


c 


C 2 


1 


a 


aA 2 


1 


b 


6B 2 


1 


c 


cC 2 



(A 2 +B 2 +C 2 + BC + CA + AB) - 



(A 2 + B 2 + C 2 +BC+CA+AB) - 



1 a A 4 

1 b B* 

1 c C 4 

1 a aA i 

1 b 5B 4 

1 c cC 4 



in connection with the numerator for the case of four arcs 



1 


a a 2 aA 


1 


b ¥ bB 


1 


c c 2 cC 


1 


d d* dD 



(A + B)(A + C)(A + D)(B + C)(B + D)(C + D) 



1 


a 


a 2 


aA 2 


M - 


1 


b 


W 


Z>B 2 




1 


c 


c 2 


cC 2 




1 


d 


d 2 


dB 2 





1 


a a 2 


aA 4 


N + 


1 


b b 2 


Z>B 4 




1 


c <? 


cC 4 




1 


d d 2 


dD 4 





a a 2 


aA 6 


b b 2 


&B 6 


G C 2 


cC 6 


d d 2 


dD 6 



p, 



* Crelle's Journ., xli. pp. 57-65 ; or Collected Math. Papers, i. pp. 540-549. 
VOL. XL. PART I. (NO. 9). 



2 E 



188 



DR THOMAS MUIR ON 



1 


a 


A 


aA 


1 


b 


B 


6B 


1 


c 


C 


cC 


1 


d 


D 


dD 


1 


a 


A 2 


aA 2 


1 


b 


B 2 


6B 2 


1 


c 


C 2 


cC 2 


1 


d 


D 2 


^D 2 



+ ABC 2 + . 


. + 2ABCD) - 


1 


a A 4 


«A 4 






1 


b B 4 


5B 4 






1 


c C 4 


cC 4 






1 


d D 4 


dD 4 



where 

M*= 2AB 2 C 2 + . . . + A 3 B 2 + . . . + A 3 BC + . . . + 3A 2 BCD + . . . , 
N = (A + B + C-f-D)(A 2 + B 2 + C 2 + D 2 ) + (ABC+BCD + CDA+DAB), 
P = A + B + C + D; 

and in connection with the denominator for the case of four arcs 

(A + B)(A + C)(A + D)(B+C)(B + D)(C + D) 



(A 2 B 2 + 



For convenience of reference these four identities may be denoted by (N 3 ), (D 3 ), 
(N 4 ), (D 4 ) respectively. No proof is given of them by Cayley, and after stating them 
he adds " mais je n'ai pas encore trouve" la loi generale de ces Equations." 

The object of the present paper is to do something to supply these wants. 

(2) In all the identities the determinants are seen to be multiplied by symmetric 
functions of as many letters as the determinants have rows or columns. A general 
theorem for the performance of such multiplications is thus seen to be desirable, and 
the following has been found. It is a generalisation of a theorem given in 1879 in the 
Transactions Roy. Soc. Edinburgh, xxix. p. 53. 

The product of a determinant of the n th order by a single symmetric function of n 
quantities a, /3, y, . . . is equal to the sum of as many determinants as there o,re terms 
in the function, each determinant of the sum being got from the given determinant and 
a term a x fiyy z . . . of the function by multiplying each element of the first row (or 
column) of the given determinant by the x th power of the corresponding one of the n 
quantities, each element of the second row (or column) by the y th power of the corre- 
sponding one of the n quantities, and so on. 

For example, 



+ 





a x a, a 
h \ I 

c. C„ l 


3 

3 


( A 2 B + A 2 C + B 2 C + B 2 A + C 2 A + C 2 B) 


I z 

a x A 2 a 2 A a 3 
&1B 2 Z> 2 B b 3 

C 1 C2 C 2 C C 3 


'3 

+ 


a x A} a 2 a 3 A 
^B 2 b 2 b 3 B 
C-y \j Co c 3 L> 


+ 


a x a 2 A 2 a 3 A 
\ 6 2 B 2 b 3 B 

C l C 2^ C 3^ 


a x A 
& X B 

C,C 


a 2 A 2 a 3 
& 2 B 2 b 3 
c 2 C 2 c s 




4 


«jA a 2 a 3 A 2 
b x B b 2 b 3 B 2 
c x C c 2 c 3 C 2 


+ 


a x a 2 A a 3 A 2 
\ b 2 B b 3 B 2 

C, Ca \J Cg \J 



The essence of the proof lies in the fact that if we single out for consideration 

* These cofactors are incorrectly printed both in the original journal and in the collection, and unfortunately 
the mistake consists in putting small letters in place of capitals. 



SOME IDENTITIES CONNECTED WITH ALTERNANTS. 



189 



any term of the determinant on the left, — the term —ajb. 2 c x say, — the corresponding 
term of each of the determinants on the right is —a^b 2 c x multiplied by a term of the 
symmetric function, the multiplying term being different for every determinant.* 

Applying this theorem to the left-hand member of Cayley's first identity, and for 
shortness' sake writing only the first line of each determinant, we have 

A 2 «A A 

which, as the first and last terms combine into one, and the second and fourth terms 
vanish, reduces to 



+ 


| A 2 a A 2 | 


+ 


| 1 aA 2 A 2 | 


+ | A aA 2 A 


+ 


| A a A 3 | 


+ 


I 1 aA A 3 | 


+ 2 j A aA A 2 



- | A 2 aA A | + | 1 aA 2 A 2 
Similarly the right-hand side becomes 



+ | A a A 3 1 + ! 1 «A A 3 



A 2 a A 2 



+ 
+ 



1 aA 2 A 2 
A a A 3 



+ 

+ 



1 a A 4 
A aA A 2 



+ 



laA A 3 
1 a A i 



which in like manner reduces to 

I 1 aA 2 A 2 | + | 1 aA A 3 



+ j A a A 3 I + I A aA A 2 



And as these two results are the same, the identity is established. 

(3) The second identity is readily proved in the same way, both sides being equal to 

| A 2 a aA 2 | + j A a aA 3 | + j 1 aA aA 3 | + | A aA aA 2 | . 

It is however essentially the same identity as the first, as may be seen on writing 
a" 1 , 6" 1 , c" 1 for a, b, c respectively in either of them. 

(4) The same method of course suffices for the proving of the third and fourth 

* Another theorem on the same subject may be illustrated by the same example, viz. : 



<h a 2 

b l b 2 


«3 
*>3 

Co 


( A^B + A 2 C + B 2 A + B 2 C + C 2 A + C 2 B) 






1 2 
C l C 2 


6 

a 3 A 2 B 
6 3 B 2 C 
c 3 C 2 A 


4 


a t a 2 a 3 A'-'C 
6 X 6 2 & 3 B 2 A 

Ci Co Co kj"ij 


+ 


a i 
h 
c i 


a 2 
h 


a 3 B 2 A 
6 3 C 2 B 
c 3 A 2 C 


«1 «2 

b i h 

C l C 2 


a 3 E 
6 3 C 
c 3 A 


2 C 
2 A 
2 B 


+ 


a t a 2 a 3 C 2 A 
&! b 2 6 3 A 2 B 
*i H %B 2 C 


+ 


a i 
b x 

c i 


a 2 
h 
c 2 


a 3 C 2 B 
6 3 A 2 C 
c 3 B 2 A 



Here only one row or column of the original determinant is multiplied, the multipliers being complete terms of the 
symmetric function. Each multiplying term, it will be observed, is used three times, and occurs in a different position 
every time ; for example, the cofactor of A 2 B on the right is 



h h 



which is equal to | a t b 2 c 3 1, as it should be. 



«1 <*2 

b l b 2 



+ 



190 



DR THOMAS MUIR ON 



identities, but the labour of writing out the products is very considerable. For example, 

the multiplier 

(A + B)(A + C)(A+D)(B + C)(B + D)(C + D) 
or 

2A 3 B 2 C + 22A 3 BCD + 22A 2 B 2 C 2 + 42A 2 B 2 CD 

on the left-hand side of (N 4 ) gives rise to 24 + 4 + 4 + 6 determinant terms, which how- 
ever reduce to 22, viz. : 



A 3 aA a 2 aA 3 



+ I A 2 aA 



aA 4 



+ 2 1 A 2 a a 2 A 2 aA 3 | 
+ | A aA 2 a 2 «A 4 | 
+ | A aA a 2 A 3 aA 2 I 



+ | A 3 a a 2 A 2 aA 2 | + | A 3 a a 2 A aA 3 | 

+ | A 2 a a 2 A aA* | + \ A 2 a a 2 A 3 aA 2 \ 

+ 2 | A 2 aA a 2 A 2 aA 2 \ + 3 | A 2 aA a 2 A aA 3 1 

+ | A a a 2 A 3 aA 3 | + I A a a 2 A 2 aA 4 | 

+ 2 | A aA a 2 A a A* | + 2 | A aA 2 a 2 A aA 3 \ 



+ | A 3 aA a 2 A aA 2 
+ |A 2 aA 2 a 2 aA 3 



+ 3 | A aA a 2 A 2 aA 3 



+ |1 «A 2 ft 2 AaA 4 | + |1 aAa 2 A 3 aA 3 | + |1 aA a 2 A 2 aA 4 | + | 1 aA 2 a 2 A 2 aA 3 |; 

and the result of multiplication on the right-hand side is 64 determinant terms which 
reduce to the same 22. 

In the case of (D 4 ) still further reduction on both sides is possible, viz., to 13 terms ; 
but it is quite clear that little is to be hoped for from this method when determinants 
of higher order than the fourth come to be dealt with. 



(5) A most important simplification of the form of the identities is suggested on 
noticing that the multipliers in (N 3 ), 

(B + C)(C+A)(A+B) and A 2 + B 2 + C 2 + BC + CA + AB, 

are each expressible as the quotient of an alternant by the difference-product of 
A, B, C, viz. : 



and 



(B + C)(C + A)(A+B) = 



A 2 + B 2 + C 2 + BC + CA + AB = 



1 


A 2 


A 4 


1 


B 2 


B 4 


1 


C 2 


C 4 


1 


A 


A 4 


1 


B 


B 4 


1 


C 


C 4 



1 


A 


A 2 


1 


B 


B 2 


1 


C 


C 2 


1 


A 


A 2 


1 


B 


B 2 


1 


C 


C 2 



When these new expressions are substituted, multiplication of both sides by the common 
denominator J A°B 1 C 2 | gives (N 3 ) in the form 



= 0, 



1 a A 




1 A 2 A 4 




1 a A 2 




1 A A 4 




1 a A 4 




1 A A 2 


1 b B 




1 B 2 B 4 


— 


1 b B 2 




IBB 4 


+ 


1 b B 4 




1 B B2 


1 c C 




1 C 2 C 4 




1 c C 2 




1 C C 4 




1 c C 4 




ICC 2 



and (D 3 ) in the form 



1 a a A 1 


1 A 2 A 4 




1 a aA 2 




1 A A 4 




1 a aA* 




1 A A 2 


16 6B . 


1 B 2 B 4 


— 


1 b bB 2 




IBB 4 


+ 


1 b bB* 




IBB 2 


1 c cC 


1 C 2 C 4 




1 e cC 2 




1 C C 4 




1 c cC 4 




ICC 2 



= 0. 



SOME IDENTITIES CONNECTED WITH ALTERNANTS. 



191 



This transformation makes a totally different mode of proof possible : for, seeking 
for a vanishing determinant of the sixth order which can be expanded into the left-hand 
member of (N 3 ) by Laplace's theorem, we easily obtain 



Similarly the manifest identity 



gives at once (D 3 ). 



1 


a 


A 


A 2 


A 4 


1 


1 


b 


B 


B 2 


B 4 


1 


1 


c 


C 


C 2 


C 4 


1 


. 


. 


A 


A 2 


A 4 


1 




. 


B 


B 2 


B 4 


1 


• 


• 


C 


C 2 


C 4 


1 


1 


a 


aA 


aA 2 


aA 4 


a 


1 


b 


6B 


&B 2 


SB 4 


I 


1 


c 


cC 


cC 2 


cC 4 


c 




. 


A 


A 2 


A 4 


1 


. 




B 


B 2 


B 4 


1 


m 


m 


C 


C 2 


C 4 


1 



= 



(6) Here, as is usual, a really appropriate proof makes generalisation easy. It i& 
readily seen that the vanishing of the latter determinant of the sixth order is not 
dependent on the values of the elements in the first half of the first and second columns. 
Substituting therefore h, h, I for 1, 1, 1 and m, n, r for a, b, c in these columns we 
still have 



h 


m 


«A 


aA 2 


«A 4 


a 




h 


m 


. 


. 


. 




k 


n 


bE 


6B 2 


6B 4 


b 




k 


n 


. 




. 




I 


r 


cC 


cC 2 


cC 4 


c 




I 


r 


. 




. 


, 


. 


. 


A 


A 2 


A 4 


1 


— 






A 


A 2 


A 4 


1 






B 


B 2 


B 4 


1 




, 




B 


B 2 


B 4 


1 






C 


C 2 


C 4 


1 








C 


C 2 


C 4 


1 



and therefore 



= 0, 



+ 



h m aA 

k n bB 

I r cC 

h m aA 4 

k n &B 4 

I r cC 4 



1 


A 2 


A 4 




1 


B 2 


B 4 


— 


1 


C 2 


C 4 




1 


A 


A 2 




1 


B 


B 2 


— 


1 


C 


C 2 





h 


m 


aA 2 




k 


n 


&B 2 




I 


r 


cC 2 




h 


m 


a 




k 


71 


b 




I 


r 


c 





1 A A 4 
IBB 4 

ICC 4 

A A 2 A 4 
B B 2 B 4 

C C 2 C 4 



On putting h, h, I = 1, 1, 1 and m, n, r = a, b, c, we have (D 3 ), and on putting 
h, k,l = 1, 1, l and a, b, c = 1, 1, 1 we have (N 3 ). 

A still further generalisation lies in the change of the exponents of A, B, C into 
suffixes, the vanishing of the determinant of the sixth order being independent of the 
meaning assigned to A n . 



192 



DR THOMAS MUIR ON 



(7) Turning now to (N 4 ) and (D 4 ) we find the same alteration of their form possible. 
From the theory of alternants it is known that 



A°B 2 C 4 D 6 
A o B i C 2 D 6 

AOB^D 6 
A o B i C 2 D 4 

A°B 1 C*D 6 



A B l O 2 D 3 , 

A B 1 C 2 D 3 

A B 1 C 2 D 3 

A^CPD 3 

A B1C 2 D 3 , 



(D + C)(D + B)(D + A)(C + B)(C + A)(B + A), 
= 2A 3 + 2A 2 B + 2ABC , 
= 2A 3 B 2 + 2A 3 BC + 22A 2 B 2 C + 32A 2 BCD , 
- A + B + C + D, 
= 2A 2 B 2 + 2 A*BC + 2ABCD . 



Substituting for these expressions on the right and then multiplying by | A°B 1 C 2 D 3 
we find (N 4 ) in the form 



- 



+ 



1 a a 2 aA 

1 b b 2 bB 

1 c c 2 cC 

1 d d 2 dD 



a 


a 2 


aA* 




b 


b 2 


5B 4 




c 


c 2 


cC 4 




d 


d 2 


dD* 





and (D 4 ) in the form 



= 



1 a A aA 

1 b B bB 

1 c C cC 

1 d D dD 



1 A 2 A 4 A 6 

1 B 2 B 4 B 6 

1 C 2 C 4 C 6 

1 D 2 D 4 D 6 

1 A A 2 A 6 

IB B 2 B 6 

1 C C 2 C 6 

ID D 2 D 6 



1 A 2 A 4 A 6 

1 B 2 B 4 B 6 

1 C 2 C 4 C 6 

1 D 2 D 4 D 6 



+ 



1 a 


a 2 


aA 2 




1 


A 


A 4 


A 6 


1 b 


V 


6B 2 




1 


B 


B 4 


B 6 


1 c 


c 2 


cC 2 




1 


C 


C 4 


C 6 


1 d 


d 2 


dD 2 




1 


D 


D 4 


D 6 


1 a 


a 2 


aA 6 




1 


A 


A 2 


A 4 


1 b 


b 2 


bB 6 




1 


B 


B 2 


B 4 


1 c 


c 2 


cC 6 




1 


C 


C 2 


C 4 


1 d 


d 2 


dD 6 




1 


D 


D 2 


D 4 


1 a 


A 2 


aA 2 




1 


A 


A 4 


A 5 


1 b 


B 2 


bB 2 




. 1 


B 


B 4 


B 5 


1 c 


C 2 


cC 2 




1 


C 


C 4 


C 5 


1 d 


D 2 


dD 2 




1 


D 


D 4 


D 5 


1 a 


A 4 


aA 4 




1 


A 


A2 


A 3 


1 b 


B 4 


bB i 




1 


B 


B 2 


B 3 


1 c 


C 4 


cC 4 




1 


C 


C 2 


C 3 


1 d 


D 4 


dD* 




1 


D 


D 2 


D 3 



(8) In its new form (N 4 ) can be as easily proved and generalised as (N 3 ). Pro- 
ceeding at once to the generalisation, we have clearty 



m. 



n. 



m 2 m 3 aA 1 aA 2 aA 4 aA 6 aA 
n 2 n % bB 1 bB 2 bB 4 
r 2 r 3 cC x cC 2 cC 4 



s 1 s 2 s 3 dD 1 dD 2 dD i 






B. 



A 4 

B 4 

Cj C 2 C 4 
Di D 2 D 4 



&B 6 
cG 6 
dD 6 
A 6 
B 6 
C 6 
D R 



bB 

cG 

dD„ 



B, 



D„ 



= 0, 



and therefore 



= - 



m x m 2 m % aA x 

n i n 2 n 3 ^B x 

r, r 2 r 3 cCj 

h s 2 h dl) i 



A A 2 A 4 A 6 
B B 2 B 4 B c 



C G 2 C 4 C 
D D 2 D 4 D 



+ 



m i m 2 m 3 ftj ^2 

5B 
cC 



■3 ^B 2 



s 3 dD 2 



^0 A-l ^-4 ^-6 

B B x B 4 B 6 
C C x C 4 C 6 
Do D x D 4 D 6 



SOME IDENTITIES CONNECTED WITH ALTERNANTS. 



193 



m x m 2 m s aA 4 
n x n 2 n s &B 4 
r i r 2 r s cC i 

S-i So So CvUi 




A A l A 2 Ag 
B B x B 2 B 6 
C C x C 2 C 6 
D D, D 2 D 6 


+ 

+ 


m 1 m 2 m 3 «A 6 
% x n 2 n % 6B 6 
r i »"« r s c Cg 

S l S 2 S 3 ^Dg 

w^ m 2 m 3 «A 

«1 » 2 W S &B 
*1 ^2 r 3 CC 

S l S 2 S 3 °^0 




A Q Aj A 2 A 4 
B B x B 2 B 4 
C C x C 2 C 4 
Do Di D 2 D 4 

A x A 2 A 4 A 6 
B x B 2 B 4 B 6 
Cj C 2 C 4 C 6 
Di D 2 D 4 D 6 



Changing the suffixes of the capital letters into exponents, and putting 



we obtain (N 4 ). 



m 1 ,n 1 ,r 1 ,s 1 = 1,1,1,1, 
ra 2 , n 2 , r 2 , s 2 = a , b , c , d , 
m 3 , n 3 , r 3 , s 3 = a 2 , & 2 , c 2 , d 2 , 



(9) The insertion of particular values in the same general identity will not however 
give (D 4 ), oi' anything resembling it. In fact it would seem that (D 4 ), although from 
other points of view simpler than (N 4 ), cannot be proved in this way at all, — that is to 
say, from ai vanishing determinant of the 8th order by the use of Laplace's expansion- 
theorem, — the first factors of the determinant products containing as many as eight 

columns, 

1 a A aA A 2 aA 2 A 4 aA i 

1 b B SB B 2 6B 2 B 4 6B 4 

1 c C cC C 2 cC 2 O cC 4 

1 d D e/P D 2 rfD 2 D 4 eZD 4 ; 

and the second factors as many as seven, 

1 A A 2 A 3 A 4 A 5 A 6 

1 B B 2 B 3 B 4 B 5 B 6 

1 C C 2 C 3 C 4 C 5 C 6 

1 D D 2 D 3 D 4 D 5 D 6 ; 

so that if a determinant of the 8th order were formed with these, the number of resulting 
products instead of being fewer than in the case of (N 4 ) would be far greater. 



(10) There is still a third form which the identities may be made to take, and from 
which it was reasonable to expect something in the way of suggestion for a new mode 
of proof. This is obtained from the previous form, — that is to say, the form which we 
have just been considering, — by performing the determinant multiplications there 
indicated. In the original form the identities consisted of terms each of which was the 
product of a determinant and a symmetric function : then they were changed into 
vanishing aggregates of products of pairs of determinants : and now by a further change 
they appear as vanishing aggregates of single determinants. 

A little examination shows that it is essential in performing the determinant multi- 



194 



DR THOMAS MUIR ON 



plications that the lines multiplied in the process shall both be columns ; — that, for 
example, instead of multiplying 



1 a A 




1 b B 


by 


1 c C 





A 2 
B 2 
C 2 



A 4 
B 4 
C 4 



which, strictly speaking, would give 



1 + a + A 
1 + b+B 
l+c+C 



A 2 +aB 2 + AC 2 
A 2 +Z>B 2 +BC 2 
A 2 +cB 2 + C 3 



A 4 +aB 4 + AC 4 
A 4 +6B 4 + BC 4 

A 4 +cB 4 + C 5 



we first change the multiplicand into its conjugate with the result that the product 
takes the form 







3 
a + b + e 
A+B + C 


A 2 + B 2 +C 2 

aA 2 + &B 2 +cC 2 

A 3 + B 3 + C 3 


A 4 + B 4 +C 4 

aA 4 +Z>B 4 +cC 4 

A 5 + B 5 + C 5 




Doing this (N 3 ) becomes 










3 2A 2 2A 4 
2a 2aA 2 2aA 4 
2A 2A 3 2A 5 


— 


3 2A 2A 4 
2a 2aA 2aA 4 
2A 2 2A 3 2A 6 


+ 


3 2A 
2a 2aA 
2A 4 2A 5 


2A 2 

2aA 2 

2A 6 


and (D 3 ) becomes 










3 2A 2 2 
2a 2aA 2 2< 
2aA 2«A 3 2< 


A 4 

*A 4 
*A 5 


— 


3 2A 2A* 
2a 2aA 2aA 4 
2aA 2 2aA 3 2aA 6 


+ 


3 2A 2A 2 
2a 2aA 2aA 2 
2aA 4 2aA 5 2aA 6 



= 0. 



(11) Now in the former of these although three determinants occur each with nine 
elements, the number of different elements is only two more than the number in a 
single determinant. Putting therefore | a 1 b 2 c 3 | in place of the first determinant and 
£ 1( £ 2 m place of the two additional elements found elsewhere, let us investigate the 
aggregate thus formed, viz. the aggregate 



a x c x a 3 




\ ii \ 


+ 


a 2 C 2 ?2 





a„ 



1 






Clearly the terms involving c 2 in the first determinant are cancelled by those in the 
second, the terms involving c 3 in the first by those in the third, and the terms involving 
£ 2 in the second by those in the third. The aggregate may thus be legitimately replaced 
by 







«3 







£l ^3 


+ 


a i c i 


a 2 


and therefore by 


h • 




a 2 




a 3 . . 


c i 


a 2 *3 — 
h h 1 


a 2 


C l a 3 


+ a 3 


C l a 2 




which manifestly va 


nishes. 

















SOME IDENTITIES CONNECTED WITH ALTERNANTS. 



195: 



(12) The identity thus obtained is of course more general than (N 3 ), because it holds 
when the eleven different elements involved in it are quite independent of one another. 
Passing over (D 3 ) let us at once try the process on the very general theorem of § 6 which 
includes both (N 3 ) and (D 3 ). The aggregate then to be considered is 



Xh 2&A 2 


2&A 4 




2m 2mA 2 


2mA 4 


— 


2aA 2aA 3 


2aA 5 





+ 



ZA 


2&A 


2AA 4 




2m 


2mA 


2mA 4 




2aA 2 


2aA 3 


2aA 6 




2h 


2AA 


2&A 2 




2m 


2mA 


2mA 2 


— 


2aA 4 


2aA 5 


2aA 6 





2AA 


2AA 2 


2/iA 4 


2mA 


2mA 2 


2mA 4 


2aA 


ZaA 2 


2«A 4 



where the number of different elements is now five more than the number in any one of 
its four determinants. Replacing these five elements by £j, £ 2 , £ 3 , £ 4 , £ 5 , and the first 
determinant by | ctib 2 c 3 j we obtain 



\ h 



and see that the terms in c x , c 



£i 





«I £l 


+ 


h £2 




£5 H 



£i 


«2 


£ 2 


\ 


c i 


£s 



c 3 in the first determinant are cancelled by those in 
Cj, c 2 , c 3 in the 4th, 2nd, 3rd determinants respectively ; so that the aggregate reduces to 



ii a s 




a i £l a 2 


& 


£2 h 


+ 


h £2 \ 


- \ £2 


• & 




& • £* 





&3 €5 

which by reason of the terms in £ 3 , £ 4 , £ 5 cancelling themselves reduces further to zero. 

Strange to say, the general vanishing aggregate to which we have thus been led for 
the purpose of establishing Cayley's identities (N 3 ), (D 3 ) is essentially the same as that 
to which a study of Kronecker's theorem regarding the minors of an axisymmetrie 
determinant brought me in 1888 (see Proc. Roy. Soc. Edinb., xv. pp. 96-98). As a 
foundation of two important theorems of so diverse a character the said vanishing 
aggregate becomes of considerable interest. 

(13) Turning now to (N 4 ) and (D 4 ) let us take the latter first, because although it 
proved recalcitrant to the previous method, it ought to yield more readily than (N 4 ) to 
the present method, if it yield at all. The new form of it is 



4 2a 


2A 


2aA 




4 


2a 


2A 4 


2aA 4 


2A 2 2aA 2 


2A 3 


2aA 3 




2A 


2aA 


2A 5 


2aA 5 


2A 4 2aA 4 


2A 5 


2aA 5 


+ 


2A 2 


2aA 2 


2A 6 


2aA 6 


2A 6 2«A 6 


2A 7 


2aA 7 




2A 3 


2aA 3 


2A 7 


2aA 7 








4 


2a 


2A 2 


2aA 2 








2A 


2aA 


2A 3 


2aA 3 








2A 4 


ZaA 4 


2A 6 


2aA 6 










2A 5 


2aA 5 


2A 7 


2aA 7 



= 0, 



VOL. XL. PART I. (NO. 9). 



2 F 



196 



DR THOMAS MUIR ON 



where, be it observed, the number of different elements in the three determinants is only 
1 6, that is to say, exactly the number in any single one of them. Replacing therefore 
the first of them by | a l b 2 c 3 d i | we obtain for investigation the more general aggregate 



Oj a 9 a 3 a i 

b 1 b., b 3 Z> 4 



a* a. 



a x 


H 


\ 


\ 


a 3 


a 4 


h 


h 


c i 


C 2 


*i 


d 2 


h 


h 


d 3 


** 



\ \ d x d 2 

d x d 2 d 3 d i i b s b i d 3 d i 

i 

Expressing each of the three determinants as an aggregate of products of complementary 
minors formed from the first two columns and the last two columns we see that 

the 1st product of the 1st determinant 
2nd 1st 



are cancelled by 



. 5th 

. 6th 

. 1st 

. 6th 



.. 1st 
.. 1st 
.. 2nd 
.. 2nd 



the 2nd product of the 2nd determinant 
2nd 3rd 



. 5th 

. 5th 

. 1st 

. 6th 



.. 3rd 

.. 2nd 

.. 3rd 

. .. 3rd 



respectively. Only six products are thus left, viz., the 3rd and 4th of each determinant, 
the aggregate of the six being 



a x 


a 2 




h 


\ 


+ 


[ h 


\ 




<h 


a 4 




a, 


a ? 




C 3 


C 4 


<h 


d 2 




C 3 


c i 


\ c x 


C 2 




d 3 


d A 


+ 


h 


\ 




d x 


d 2 


H 


« 4 




C l 


C 2 




! a x 


«2 




K 




a s 


a i | 


h 


K 


\ 


\ 




d 3 


d, 




1 c 3 


C 4 




d x 


d 2 




c i 


C 2 




d 3 


d i 



+ 

which is nothing more than the double of zero in the form of the well-known vanishing 
aggregate 

I cti£ g I • I a 3 /3 4 | - ! ai /3 3 I • I a 2 /3 4 | + | ai /3 4 I • I aj3 3 \ . 

(14) The new form of (N 4 ) is 



+ 



4 


2A 2 


2A 4 


2A 6 




4 


2A 


2A 4 


2A 6 


2a 


2aA 2 


2aA 4 


2aA 6 




2a 


2aA 


2aA 4 


2aA 6 


2a 8 


2a 2 A 2 


2a 2 A 4 


2a 2 A 6 




2a 2 


2a 2 A 


2a 2 A 4 


2a 2 A 6 


2aA 


2aA* 


2aA 5 


2aA 7 




2aA 2 


2aA 3 


2aA 6 


2aA 8 


4 


2A 


2A 2 


2A 6 




4 


2A 


2A 2 


2A 4 


2a 


2aA 


2aA 2 


2aA« 




2a 


2aA 


2aA 2 


2aA 4 


2a 2 


2a 2 A 


2a 2 A 2 


2a 2 A 6 




2a 2 


2a 2 A 


2a 2 A 2 


2a 2 A 4 


2aA 4 


2aA 5 


2aA 6 


2aA 10 




2aA 6 


2aA 7 


2«A 8 


2aA 10 



= o, 



where now the number of different elements is 20, — that is to say, four more than the 
number in any single determinant. Replacing these four elements by £ x , £ 2 , £ 3 , £ 4 , 



SOME IDENTITIES CONNECTED WITH ALTERNANTS. 



197 



and the first determinant by | a 1 b 2 c s d i | we obtain for investigation the more general 
aggregate 



a i «2 a 3 a i 

\ b 2 b 3 5 4 

C l C 2 C 3 C 4 

d x d. 2 d 3 d i 



ii a s 



\ d 1 



\ d 2 



C 4 



a i ii a 2 
\ d x b 2 & 4 



h d 3 



K L 



£ 


a 2 


«3 


d x 


h 


h 


A 


C 2 


C i 


d 4 


& 


£ 



Now it is readily seen that 

the cofactor of d„ in the 1st determinant 



are cancelled by 



d 3 
h 



1st 

1st 

2nd 

2nd 

3rd 



the cofactor of d 2 in the 2nd determinant 



"3 

h 



3rd 
4th 
4th 
3rd 

4th 



respectively. All therefore that is left in each determinant is one element accompanied 
by its cofactor, viz., the element in the place (41) ; so that the aggregate with which we 
started is reduced to 



-d, 



a 2 


H 


a 4 


+ \ 


\ 


h 


\ 




h 


c s 


C 4 





€l «3 a i 



£Z C 3 C 4 



I di K 

1 fc 2 C 2 



+ K 



ii a 2 

di \ 

fc2 C 2 



which again is clearly equivalent to 



fcl a 2 a Z a i 



and therefore vanishes. 



d x b 2 



d 1 b 2 



(15) This identity is not new, being simply a special instance of the fourth-order 
case of the theorem above referred to as having been used in proving Kronecker's 
relation between the minors of an axisymmetric determinant. (N 3 ), (D 3 ), (N 4 ) are thus 
seen to be dependent on the same theorem. The full expression for | a 1 6 2 c 3 c? 4 I is 



a x 


a 2 


a 3 a 5 




«1 


\ 


\ 


^3 & 


+ 


\ 


c i 


H 


c 3 y 5 


C l 


»U 


D 2 4 


D 34 d i 




D K 



c 2 y 5 

D„„ d Q D 



+ 



u 



a x 


a 5 


a s 


a 4 




«5 


a 2 


H 


a i 


\ 


& 


h 


K 


+ 


A 


\ 


\ 


h 


c i 


75 


h 


c i 


75 


C 2 


C 3 


c i 


D 12 


d 2 


I>23 


E»24 




*1 


D12 


D» 


D M 



198 



DR THOMAS MUTR ON 



where the elements which may be all different are 

the [n 2 , which here is] 4 2 elements of | a 1 b 2 c 3 d i | , 

the [n—l, which here is] 3 elements a 5 , /3 5 , <y 5 , 

and the [^n(n — 1), which here is] 6 elements D 12 , D 13 , D 14 , 

^23> ^24 ' 



'34 



This degenerates into the identity of the preceding paragraph if we put D 12 , D 13 , D 14 

= & 2 ' h » bi ; D 23 = ^4 5 ft = ^i • 

(16) Having thus the general fourth-order theorem of which (N 4 ) is a case, it is 
natural to inquire whether there be a corresponding general fourth-order theorem of 
which (D 4 ) is a case. The following new result regarding the sum of two determinants 
of the fourth order gives the answer to this inquiry : — 

If | a 1 b 2 c 3 d 4 | , | a 1 /3 2 y 3 ^ 4 | be any two fourth-order determinants, their sum is 
equal to the sum of six determinants, each of which contains a pair of complementary 
minors from each of the originals, viz., the sum 



+ 



a i a 2 


73 


74 




a x 


a 2 


ft 


ft 




a x 


a 2 


«3 


a 4 


b x b 2 

a X «2 


^3 
C 3 


<*4 
C 4 


+ 


«1 
c l 


a 2 

C 2 


b 3 
«5 3 


b 4 

^4 


+ 


ft 

7i 


ft 

72 


b 3 

C 3 


b 4 

C 4 


ft ft 


d 3 


d, 




7i 


72 


d 3 


d 4 




dx 


d 2 


K 


<?4 


«X «2 


a 3 


a 4 




ft 


ft 


S 3 


a 4 




7x 


72 


a 3 


a 4 


\ b 2 

C X C 2 


ft 
73 


ft 
74 


+ 


«x 


b 2 

<*2 


«3 

C 3 


«4 

C 4 


+ 


*x 
c x 


<?2 
C 2 


b 3 

«3 


b 4 
a 4 


s, s 2 


d 3 


^ 




dx 


d 2 


73 


74 




dx 


d 2 


ft 


ft 



Expressing each of the six as an aggregate of products of complementary minors, we 
have the sum equal to an aggregate of thirty-six products, viz. : 





«X «2 


C 3 C 4 


- 


&•* din 
a X a 2 


&, 5 4 

d 3 d 4 


+ 


a x a 2 
ft ft 


&$ ^4 

C 3 C 4 


+ 


«X «2 


73 74 


- 


ft ft 


73 74 

c 3 c 4 


+ 


«X a 2 

Iftftl 


y 3 y4 
Is, si 


+ 


«x « 2 | 

a l «2l 


S 3 <$ 4 

d s d i 


a x a 2 
i c 1 c 2 




+ 


a x a 2 
7x7 2 


& 3 & 4 

S 3 Si 


+ 


«X a 2 
C X C 2' 


ft ft 

d 3 d t 


- 


«x « 2 
7x72 


ft ft 

<5 3 5 4 


+ 


C l C 2| 

7x7 2 l 


6 3 &J 


«x« 2 

ft ft 


6 :i C 4 

5 3 Si 


- 


7x7 2 


s 3 s 4 


+ 


a x a 2 


c 3 c 4 


+ 


ft ft 

7x72 


a 3 a 4 


— 


ft ft 
d x d 2 


«3 a 4 

c 3 c 4 


+ 


7x7 2 
d x d 2 


«3 a 4 
^3* 4 


+ 


«x <* 2 


73 74 

rf 3 d 4 


— 


a x a 2 

C X C 2 


ft ft 

^3 d i 


+ 


«X «2 

<?X <*2 


ft ft 

73 74 


+ 


c x c 2 \ 


a 3 a 4 
rf 3 rf 4 


— 


S x S 2 


a 3 a 4 

73 74 


+ 


c x c 2 


o 3 a 4 

ft A 


+ 


ft ft 
»1 h 


C 3 C 4 

7(74 


— 


ft ft> k «4 

S 1 S 2 \\ y 3 y 4 


+ 


ftft| 

<^ d 2 \ 


a 3 a 4 

c 3 c 4 


+ 


$1 ^2 


a 3 a 4 

73 74 


— . 


d t d 2 


c 3 c 4 


+ 


S x S 2 
d x d 2 


a 3 a, 
a 3 a 4 


+ 


7i7 2 

^1 ^2 


! Og «4 

ft ft 


- 


7i7> 

C X C 2 


ft ft 


+ 


7x72 
rfj c£ 2 


& 8 *4 

a 3 a 4 


+ 


s x s 2 

h C 2 


a 3 a 4 

ft ft 


- 


d x d 2 \ 


a 3 a 4 
a 3 a 4 


+ 


d x d 2 \ 


j a3 a 4 
1 63 J, . 



SOME IDENTITIES CONNECTED WITH ALTERNANTS. 



199 



A little examination of this square array brings out the fact that all its terms cancel 
each other with the exception of those which are situated in either diagonal, and that 
the cancellation takes place in a pleasingly symmetrical fashion, each non-diagonal term 
and its conjugately situated fellow annihilating one another. Further, the aggregate of 
the six terms in the principal diagonal is seen to be 

and the aggregate of the six terms in the secondary diagonal to be 

I «i & y* ^ I ; 

so that the theorem is established. 

Now turning to the identity of § 13, which, as we have noted, has no elements 
different from the sixteen composing a single one of the determinants involved in it, we 
see at once that if it is to be included in that just found, the elements of the second 
parent determinant of the latter must be the same as the elements of the first. Making 
them the same even in form we obtain the nugatory result 

2 | a&c^ | = 2 | ajb&fli \ . 

But making the consanguinity less pronounced, the second parent being of the form 
| a^^d^ | , we find that only the 3rd and 4th of the progeny are of no account, and 
that the 6th and 5th are the same as the 1st and 2nd respectively : so that after 
division by 2 there results 



a x 


a. y 


a z 


a i 




\ 


h 


\ 


K 




c i 


C 2 


C 3 


C 4 




d x 


d 2 


d 3 


d, 





«i 


H 


c i 


H 




h 


\ 


4 


d 2 


+ 


% 


a t 


h 


C 4 




h 


K 


d 3 


d, 





a. y 



h K 

d 1 d 2 
d d A 



which completely agrees with the identity of § 13. 



(17) A fourth method of investigation consists in making transformations which 
result in the segregation of the capital letters from the small letters. As, however, 
nothing new results from it in the case of (N 3 ), (D 3 ), (N 4 ), its application to (D 4 ) is all 
that need be given. 

The aggregate to be considered in this case is 



1 


a A 


aA. 


1 


b B 


m 


1 


c C 


cQ 


1 


d D 


dD 



A°B 2 C 4 D 6 I - 



1 


a 


A 


aA 2 


1 


b 


B 


6B 2 


1 


c 


C 


cC 2 


1 


d 


D 


^D 2 



A B 1 C 4D5 I + 



1 a A 4 aA 4 
1 b B 4 &B 4 
1 e C 4 cC 4 



d D 4 dD* 



A o B i C 2 D 3 1 



Now each of the first factors of the three determinant products here appearing is of the 
form 

1 a A w aA" 

1 b B w 5B" 

1 c C" cC» 

1 d D w dr>« 



200 



DR THOMAS MUIR ON 



+ 



which is easily seen to be transformable into 



1 a 
1 b 



1 c 



J.(OD«+A»B») - 



1 a 
1 c 



1 b 
1 d 



(B-D- + A-C") + L ^ 



1 b 
1 c 



(B"O + A«0>). 



The aggregate under consideration can thus be changed into 

} a A.\ C A {(CD + ABVI A°B 2 C 4 D 6 | - (C 2 D 2 + A 2 B 2 )-| AOB^D 5 1 + (C 4 D 4 +A 4 B 4 )- 1 A^CD* 
1 o I I 1 d | ( 



1 a 

1 c 

1 a 

1 d 



. I h I • | (BD+ AC) • | A°B 2 C 4 D 6 \ - (B 2 D 2 + A 2 C 2 ) • | AOB^D 5 | + (B*D 4 + A 4 C 4 ) • | A^C 2 !) 8 
{ (BC+AB) • | A°B 2 C 4 D 6 1 - (B 2 C 2 + A 2 B 2 ) . | A°B 1 C*D 8 1 + (B 4 C 4 + A 4 B 4 ) • | AOB^D 3 



1 c 



and this can only vanish identically when the three expressions enclosed in { } are 
equal, for the cofactor of bd is the difference between the first and third, and the cofactor 
of be is the difference between the first and the second. Now the sum of the said three 
expressions is 

! A°B 2 C 4 D 6 j-2AB - | A^OD^-SA^* + | AOB^D 3 1 • 2A 4 B 4 , 

and this by the theorem for the multiplication of an alternant by a symmetric function 
of its variables is found to be 

3|A°B 3 C 5 D 6 | + 3|AB 2 C 4 D 7 |. 
Consequently each of the three is equal to 

| A°B 3 C 5 D 6 | + | AB 2 C 4 D 7 | * 
The aggregate above reached can thus be changed into 



and therefore into 



1 a 
1 b 




1 c 

i d r 


1 a 
1 c 




1 b 
1 d 


+ 


1 a 
1 d 




1 b 
1 c 



1 • (l A°B 3 C 6 D 6 | + | AB 2 C 4 D 7 |) 



1 a 

1 b 

1 e 

1 d 



1 a 

1 b 

1 c 

1 d 



A°B 3 C 5 D<5 | + | AB 2 C 4 D 7 



')■ 



where the vanishing factor is what each of the first factors in the original aggregate 
becomes when we put A = B = C = D=1. 

* A direct proof that 

| A°B 2 C 4 D 6 | -(AB+CD) - | A°B'C 4 D 5 | • (A 2 B 2 + OD*) + | AoB'CFD 3 ! -(A 4 B 4 +C 4 D 4 ) 
= | A°B 3 C 5 D 6 | + I A 1 B' 2 C 4 D 7 | 

is obtainable from the theorem above given regarding the sum of two fourth-order determinants, the parents being 
the two determinants on the right, and the progeny the six determinants obtainable on the left by performing the 
multiplications indicated, viz. : 



A A 3 A 6 A 7 

B B 3 B B B 7 

1 C 2 C 4 C 6 

1 D 2 D 4 D 6 



1 A 2 A 4 A 6 

1 B 2 B 4 B 6 

C C 3 C 6 C 7 

D D 3 D 6 D 7 



SOME IDENTITIES CONNECTED WITH ALTERNANTS. 



201 



The corresponding results for (N 3 ), (D 3 ), (N 4 ) are 



1 a 1 




1 a a 




1 a 1 a 




1 b 1 
1 c 1 


| A^C 4 i , 


1 b b 
lee 


| A*B 2 C 4 1 , 


1 b 1 b 
1 c 1 c 
1 cl I d 


| A^OD* 



as may also be seen from §§ 6, 8. 

(18) The problem of finding, for determinants of a higher order than the fourth, 
identities similar to Cayley's I do not at present enter upon : like Cayley, " je n'ai pas 
encore trouve" la loi general e de ces equations." I content myself with stating the 
problem in as simple a form as possible. 

To express each of the products 



For the fifth and sixth orders it is : — 



I 1 

I 1 



A aA 
aA a 2 A 



a a 2 A aA a 2 A 



A°B 2 C 4 D 6 E 8 | 
A°B 2 C 4 D 6 E 8 F 10 

A B 2 C 4 D 6 E 8 F 10 



as aggregates of products of a similar hind, the first factor of each product on the 
right of the identity being formable from the corresponding factor on the left by replac- 
ing A by an even power of A, B by the same even power of B, and so on. 
For example, and more definitely, to determine a, /3, y, 8, e, £, t], 6, so that 

| 1 a a 2 A aA | • | A°B 2 C 4 D 6 E 8 I = I 1 a a 2 A 2 aA 2 | • | A°B a C^DvE« | 

±|1 a a 2 A 4 aA 4 | • | A B<CO>E 9 | 
±11 a a 2 A 6 aA 6 | • 1 A^C^E 4 |. 



( 203 ) 



X. — The Hessian of a General Determinant. 
By Thomas Muir, LL.D. 

(Read January 21, 1901.) 

(1) There being n 2 independent variables in a general n-line determinant, the Hessian 
of the determinant with respect to the said variables must be a determinant with n 2 
lines : and as a general w-line determinant has all its terms linear in the elements 
involved, it follows that each element of the Hessian being a second differential- 
quotient cannot be of a higher degree in the variables than the (n — 2) th , and that 
consequently the degree of the Hessian itself cannot exceed n 2 (n — 2). The object of 
the present short paper is to show that this degree is attained by the n(n— 2) th power 
of the given determinant being a factor of the Hessian. 

(2) Beginning with the case of n = 3, let the originating determinant be 



Co 



a., 



so that single differentiation with respect to the nine elements produces 



he* 



l 3H 

- I a 2 e s I , 



a bo 



- I h t- I 

I a i C 3 I ' 

- | a x b 3 | , 



- a.&, 



I «AU 



"1 » 2 ' 3 

Bj, B,, B 3 say. 

Cj , C. 2 , C 3 



These being each differentiated in the same way, i.e. with respect to each of the nine 

original elements, we obtain the eighty-one elements of the Hessian : and if we agree 

to take the independent variables in the order, a lt a 2 , a z ; b v b 2 , b 3 ; c v c 2 , c 3 , the 
Hessian itself will be 



-c Q 



-Ci 



c 2 
-c. 



-h 
I 





-h 


h 


h 




~h 


h 


h 






a 3 


-a 2 


a 3 




«i 


a., 


-a. 





h - h 



a 3 
-a<, 



By way of remembering its constitution we should think of it as divided into three 
equal parts by two left-to-right lines, and at the same time into three equal parts by 
VOL. XL. PART I. (NO. 10). 2 G 



204 



DE THOMAS MUIR ON 



two top-to-bottom lines. The nine small square arrays thus resulting may then be 
symbolized by 

• r -P 

-y ■ a 

fi -a 

each of the three-line matrices a, /?, y being zero-axial skew, and composed of 
elements from only one row of the original determinant. 
Now if we multiply this b}' | a 1 b 2 c s | 3 in the form 



h 



a 2 
b, 

Co 



a. 2 
b„ 



a. 2 



a, 



we obtain 



-B 2 
-B„ 



B 2 
B 3 
0, 

c. 



"A, 
-A., 

-A 3 



"A 2 
-A, 



A x 
A 2 
A, 



C x -B, 

C 2 — B 2 

Cn — Bq 



-c. 



-o 1 

-c 2 
-a 



3 

h | 
Co I 



A x 
A 2 
A 3 
B, 
B 2 
B Q 



which if divided like the multiplicand into nine three-line minors takes the form 



7 P 



-y 



Br 


-»i 


B 2 - 


-B, 


B 3 - 


"B 3 



<V 


-Ci 


C 2 - 


-c 2 


c 3 - 


-c 3 , 



-fi -a • . 

It is better however to write the three zero minors differently, viz.- 

Ax-A, . . 
A 2 -A 2 . . 
A 3 _ A 3 . . , 

for then we are able to state more easily the law of formation of the nine. Thus, we 
may then say that the three 

• 7 /?' 

have -Aj, — A 2 , -A 3 ; — B v -B 2 , -B 3 ; — C l5 -C 2 , — C 3 respectively in their first 
columns, and A v A 2 , A 3 in a column of each, the particular column being the first of the 
first, the second of the second, and the third of the third. Similarly, the next three 



-7 



THE HESSIAN OF A GENERAL DETERMINANT. 



205 



have — A ls — A 2 , — A g ; — B l5 - B 2 , — B 3 ; — C l9 — C 2 , — C 3 respectively in their second 
columns, and B l5 B 2 , B g , in a column of each ; and so in the remaining case. The 
product-determinant has thus two kinds of columns, viz., those with three non-zero 
elements, and those with six. Of the former kind there are six, and of the latter three. 
Further, when there are only three non-zero elements in a column they are all negative, 
and when there are six they are all positive. Adding together the three columns which 
have six non-zero elements, we can remove the factor 2 from the resulting column : and 
if we then diminish the two other columns by this altered column, we shall change 
them into columns with only three non-zero elements like the rest. Our result then 
will take the form 

-Pi • 

-0, 

-c. 



A, 




-»i 


A 2 




~ B 2 


A 3 


. 


-Bi 


Bi 


-A x 




B 2 


-A 2 . 




B a 


-A s . 





"B 2 
-B. 



C, 



-A, 



-B 1 

-B, 
-B„ 



-C 2 

-c. 



-c 2 
-a 



which is easily changed further into 



(-)3 2 



Ax 

A 2 
A 3 
Ba 
B 2 
B 3 
Oi 

Co 

c. 



B t 
B 2 
B Q 



Oi 



Ax 


-B, 


Cx 


A 2 


-B 2 


c 2 


A 2 


-B 2 


c 3 



Ax 
A, 



B 2 
Bo 



"Cx 

-c 2 
-a 



by interchanging the 2nd, 3rd, 6th columns with the 4th, 7th, 8th respectively. We are 
thus led to the equation 

H ( | a, \ H | ) • | ai b 2 c 3 j" = ( - ) 5 2 | A^Cg i 3 , 

and therefore finally to 

H (lajVsk) = -2 |aA c s |3 - 

(3) Taking next the case of n = 4, the originating determinant being 



a, a a* 



h h 



t?j d 2 d 3 d i 

we obtain, from single differentiation with respect to the sixteen elements, 



206 



DR THOMAS MUIR ON 



or say 



1 h 2 c a d i 1 . 


- 1 v 3 rf 4 1 , 


1 V 2 < ? 4 1 » 


1 "l C 2^3 ' 


- 1 a 2 c 3 rf 4 | , 


Iw^li 


- | ajC 2 rf 4 1 , 


1 a l C 2 3 1 > 


1 « 2 M4 1 > 


- i <h b 4 l i i . 


1 «i& 2 ^4 ! » 


-KM 3 |. 


- | aj)^ | , 


1 « A C 4 1 . 


- 1 « A C 4 1 » 


1 «A C 3 1 » 




1 2 


A 3 A 4 






B l B 2 


Bg B 4 






C l C 2 


Cg C 4 






Di I> 2 


Dg D,. 





These being each differentiated in the same way, i.e. with respect to each of the sixteen 
original elements, we obtain the 256 elements of the Hessian ; and find the latter, when 
partitioned into 4x4 minor matrices of the 4th order, to be of the form 



where (a,/3), (a, r ), 



(a,(3) = 



(y,S) 


-(AS) (Ay) 


- (y,S) 


(a,S) - (a,y) 


(AS) "(a,8) 


(«,/?) 


-(Ay) (<*,y) 


-<»,/*) 


1 exactly alike,- 


— for example 


1 «3^4 1 


- | a. 2 b 4 1 j a 2 b 3 


- 1 «3^4 1 


1 «i & 4 1 - 1 a A 


i «2 & 4 1 - 1 a A 1 


1 a A 


- 1 «2^3 1 I a A 1 


- 1 »A ! 



— being thus all zero-axial skew like their parent matrix.* 

Multiplying the Hessian by | a-fi^d^ | 4 we obtain as before a product which, when 
partitioned like the multiplicand, is of the form 



where 



- (yi a s)' - {ySaf 
-(W -(W 


(yi a s)' 
(y 2 A)' 


(V4)' 

(W 


(/W'= \ I 2 
I --^3 

l-B 4 


A, 

A 2 

A 3 • 

A 4 • 




- 



the suffix of a indicating the column in which the positive A's appear, and the suffix of 
/3 the column in which the negative B's appear. Any one of the four lines of matrices, 
sav the line 

(/V2)' (yi a s)' (Sia 4 )'» 

may consequently be described in language exactly similar to that employed in the case 



Note, too, that the determinant of every matrix vanishes, being, in the case exemplified, the square of the vanishing 
Pfaffian 



aA I I «3 6 4 I - I a A I a Jh I + I a A I I «2 6 3 1 ■ 



THE HESSIAN OF A GENERAL DETERMINANT. 



207 



where n = 3 ; and thus the product determinant comes to be transformable into 3 times 
a determinant whose first four columns are 

A, 

A 2 . 

A 3 . 

A 4 

"A 2 
"A 3 
"A 4 

-A, 

-A 2 

-A 3 

-A 4 

• "A, 
. -A 2 
. -A, 

• "A 4 

these being followed by four columns containing B's similarly placed but all negative, 
these again by four columns containing negative C's, and these by four columns contain- 
ing negative D's. Interchanging columns as before, with the necessary accompaniment 
of (3 + 2 + 1) + 3 changes of sign, we obtain 



and therefore 



H ( I ai b,c 3 d 4 | ) • ! a.b.^d, j* = ( - )93 | AjB^L^ |* , 

= (-y3\ ai hc 3 d,\v, 

H ( | a 1 b 2 c s d i | ) = - 3 | a l b i c 3 d i | 8 . 



(4) The natural generalisation for an originating determinant of order n is thus fully 
legitimised, the number of requisite changes of sign then being 

{{n-\) + (n-2) + ... + 2 + l} + (n-1), 

which of course is the same as 

(n - 2) + (n - 3) + . . . + 2 + 1, 

i.e., 

\{n - 1) (n - 2) : 
and the resulting equation is 

H ( I «i„ I ) • | flu, |" = ( - )*'"- 1,( "- 2 » • (n - 1) • I A 1B |- , 
so that 

H(|a lH |) = ( _ )i(»-D(«-2) . ( w _l) . | ain |»(n-l)-» 



= (_l)i(n-l)(ft-S) . ( w _!) . | ai . 



|n(«-2) 



VOL. XL. PART I. (NO. 10). 



2 H 



( 209 ) 



XL — The Differentiation of a Continuant. 
By Thomas Mum, LL.D. 

(Read January 21, 1901.) 



(1) The continuant 



a l 


h 




• 


-1 


°2 


h 




• 


-1 


«3 


h 






-1 


a i 



is conveniently denoted by 

K ( b i & 2 h \ or ( b l b 2 h V 
yftj a 2 a 3 a 4 / \a 1 a 2 a 3 a J ' 

and, when the elements b v b 2 , b 3 of the variable minor diagonal are each equal to 1, a 
further simplification is obtained by leaving them out ; — thus, 

K(a,b,c,d) or (a,b,c,d) 
abed + ab + ad + cd + 1. 



stands for 



(2) The general continuant, K, of the n th order is a function of not more than 2n—l 
independent variables, — n in the principal diagonal and n—1 in the variable minor 
diagonal. We thus may be expected to know the differential-quotient of the continuant 
with respect to an element in either of these diagonals. 

Taking first the case where the element is in the minor diagonal, b h say, we use the 
known identity 



c 



*i h-i b h &„_! 

a 1 a 2 . . . %_! a h a h+l . . . a n _ t a, 



_ ( &1 &A-1 \ . / ^A+1 • • • K-l \ 

V^ a 2 . . . a h _y aj \a k+1 . . . a n _-^a n ) 

+ b h ( 6 i ••• )■( ••■ b ->) 

\a x a 2 .. . a h _J \a h+2 ... a n _ aj 



to separate out the element in question, and thus see at a glance that 

9K = / b x . . . \ / b n _, \ 

db h \«i « 2 • ■ • 0>h-\) W+2 • • • a n-\ a n) ■ 

In other words, the differential-quotient of K with respect to b h is obtained 
mechanically by taking K, deleting 6 A _ l5 a h , b h , a h+1 , b h+1 from it, and inserting the 
brackets )( instead. 

Secondly, taking the case where the element is in the principal diagonal, a h say, we 
use the same identity at the outset, but go a step further and alter 

/ b x b h _ x \ . / 6 X \ / 6j \ 

\tt-L a. 2 ... a h _ x aj in ° ^ a 2 . . . a h _J h ~ l + \a x a. 2 . . . a h .J ak 

VOL. XL. PART I. (NO. 11). 2 1 



210 DR THOMAS MUIR ON 

for the purpose, as before, of separating out the element concerned, thus obtaining 

d a „ \«i « 2 ■ • • a h-J W+i ■ ■ • a «-i a J • 

In other words, the differential-quotient of K with respect to a h is obtained mechanically 
by taking K, deleting b h . lt a h , b h , and inserting the brackets )( instead. 

When one of the end elements is used as independent variable the result is of course 
simpler : thus 

3K = ( b 2 &„_ x \ 

9a } \«2 a 3 • • • a «-l a n) ) 

3K_ = / 6, &„_ s \ 

96,1-! \ a l «2 • • • a n-Z a n-i) • 

(3) It is thus seen that in whatever diagonal the independent variable is situated 
the differential-quotient of K is in general the product of two coaxial minors of K, and 
that when the independent variables are in the same row the differential- quotients have 
a factor in common. As a result of this 

( b n-i \ 

3K ^ 3K \a h+1 . . . a n _ x aJ 

3«/i 96a " ( K-i \ ' 

\ a 7i+2 • • • a n-l ®n/ 
— n 4- *+' 7) 

dk+2 + — . 

a h+3 + • . 

+ ht=i 

(4) If we differentiate dlijda h with respect to another element of the main diagonal, 
that element must be in one of the two factors of dK/da h , 

( *! ) ( & »-> ) 

\a x a^ ... a h _J , \a h+1 . . . a„_ x aJ . 

and not in the other, so that the result of the second differentiation is in general to give 
an expression of three factors. Thus if 

X = ( a Py 8 € £ 

\a b c d ef g y 
we have 

9c.9/ "" \a b) ' \d e) ' 9 • 

When the two elements used as independent variables belong to the minor diagonal, 
the like consequences ensue : it has to be noted however that if they be consecutive the 
result is 0, because when we differentiate with respect to b h , neither ^.j nor b h+1 
appears in the result. 

(5) As each term of the continuant is linear in each of the elements occurring in it, 



THE DIFFERENTIATION OF A CONTINUANT. 



211 



the differential-quotient with respect to an}^ element is the same as the cofactor of that 

element. Hence instead of 

SK 3 2 K 

da,' da h da„ +1 ' 
we may write 

cof a ln cof a h a, l+l . 

(6) When the two elements used as independent variables are consecutive in the 
main diagonal, the result is the same as is got by one differentiation with respect to an 
element of the minor diagonal. For, taking dK/da h as above, we have 

S 2 K 



da h da 



»™/!+l 



\«! a 2 . . . a,,_! 



,fflft+2 



a„_, a, 



dK 

db h 



Corroboration of this is found m the fact that one of the two-line minors of K is 



'' " or a h a, l+1 + b h , 

~ l a h+\ I 



thus ensuring that the cofactor of a h a h+1 is the same as the cofactor of b h . 

(7) When the continuant concerned has unit elements in the minor diagonal the 
rule for mechanically obtaining the differential-quotient is still simpler, the only element 
to be deleted being that which is taken as the independent variable. Thus if 

K = (a v a 2 , a s , a 4 , a 5 , a 6 , a.) 



we have 
and 



3K / W N 

— = (a v a 2 , a s , a 4 ) (a , a 7 ) , 



9 2 K 

3a ft 3a 3 



= (Oi, « 2 ) • K) • («6. %) • 



(8) The foregoing considerations have been suggested by a curious theorem which 
has turned up recently in the course of an investigation connected with Hessians. 

The Hessian, it will be remembered, is always axisymmetric : and, if the originating 
function be linear in each of the variables, its second differential-quotient with respect 
to any variable will be 0, — that is to say, the Hessian will be zero-axial as well as axi- 
symmetric. In this case, consequently, there arises a semi-quadrate array which seems 
worthy of study. 

(9) Taking the case where the originating function is K(a,b,c,d), i.e. abed + ad + cd + 
ab+l we have 

I 32R 3 2 K 8 2 K 



da.db da.de da.dd 
8 2 K 3 2 K 
db.de db.dd 

a 2 K 

dc.dd 



cd + 1 bd be+1 
ad ae 
ab + 1 



212 



DR. THOMAS MTJIR ON 



= (cd + 1) (ab+l) - hd.ac + (be + 1) ad, 
= abed + ab + cd + 1 - abed + abed + ad , 
= ~K(a,b,c,d) . 

Again, taking the case where the originating function is 

K (a,b,c,d,e,f,) 
we have our Hessian-like Pfaffian 

3 2 K 3-^ &k_ &K 3 2 K 
da.db da.de da.dd da.de da.df 
3 2 K 3 2 K 3 2 K 3 2 K 
dbFc Wdd, db.de db.df 
3 2 K 3 2 K 3 2 K 
3c.3c2 dc.de dc.df 
3 2 K 3 2 K 
3d.3e 3d.3/ 
3 2 K 
3e.3/ 

= ,(c,d,e,/) b(d,e,f) (b,c) (e,f) (b,e,d)f (b,e,d,e) 

a(d,e,f) ac(e,f) a(e,d)f a(c,d,e) 

(a,b)(e,f) (a,b)df (a,b){d,e) 

(a,b,e)f (a,b,c)e 

(a,b,e,d) 

= (c,d,e,f)da,b){e,f) (a,b)df (a,b) (d,e) 

(a,b,c)f (a,b,c)e 

(a,b,c,d) 

- b(d,e,f) I ac(e,f) a(c,d)f a(c,d,e) 

I (a,b,c)f (a,b,c)e 

(a,b,e,d) 

+ 

+ (b,c,d,e) I a(d,e,f) ac(e,f) a(e,d)f 

I (a,b) (ej) (a,b)df 

(a,b,c)f 

Now it is easily verified that the five minor Pfaffians here are equal to 

(a,6)-K, ac-'K, ad-~K, ae-K, af-~K; 

consequently the original Pfaffian 

= K{ (a,b) (c,d,e,f) - abc(d,e,f) + a(b,e)d(e,f) - a(b,c,d)ef+ a(b,c,d,e)f ] , 

= K-[ (a,b) (e,d,e,f) - {abcd(e,f) + abef) + {abcd(ej) + ad(e,f)} - a(b,e,d)ef + {a(b,e,d)ef+ a(b,c)f} ] , 

= K-[ (a,b) (c,d,e,f) - abcf+ ad(e,f) + a(b,e)f] , 

= K-[ (a,b) (c,d,e,f) + ad(e,f) + of] , 

= Kia,b,c,d,e,f) , 

= K 2 . 



(10) These two cases raise the presumption that when the originating function is 

K («l» «2> a 3> ' a ln) 






THE DIFFERENTIATION OF A CONTINUANT. 213 

the semi-Hessian of K will be 

It is clear however that before we can test this the auxiliary theorems which we have 
used in proving the first two cases must be generalised. 

(11) The first of these auxiliary theorems is that which involves the fact that all 
our minor Pfaffians of the second order contain K as a factor. What the theorem itself 
actually is becomes more apparent if we adopt the 'cofactor' notation instead of the 
notation of differential-quotients : for then the instances are — 



cof cd cof ce cof cf 

cof de cof df 

cof ef 

cof bd cof be cof bf 

cof de cof df 

cof ef 



= K-(a,b) 



= K- ac , 



Or 



cofcd.coief - coice.coidf + cof cf . cof de = ~K- (a,b) , 
cof bd . cof ef - cof be . cof df + cof bf . cof de = K- ac , 



(12) The general theorem here exemplified is — 

If K be a simple continuant of any number of elements a 1? a 2 , . . . , a n , and a, /3, y, S 
be the suffixes of any four elements taken in the order in which they occur, then 

cof a a a p . cof a y a$ - cof a a a y . cof a p as + cof a a a$ . cof a p a y 

= K • cof a a a p a y as . 

In proof of this we note in the first place that the expression on the left 

= (a v . . . , a a -i) (a a+ i, . . . , a P -\) (a p+1 , . . . , a n ) • (a 1; . . . , a y _i) (a y+ i, . . . , a S -i) (a«+i, ■ ■ ■ , a n ) 
- (a 1( . . . , a a _i) (a 0+ i, . . . , a y -i) (a y +i, . . . , a n ) ■ (a v . . . , a p .{) (a p+i , .. ., a S -i) (os+i, • ■ . , a n ) 
+ (a lt . . . , a a _i) (a a+1 , . . . , a«_i) (a g+1 , . . . , a») • (a l5 . . . , a^-i) («£+i, • • • , « v -i) (« y +i, • • • > a '0 > 

which, on account of there being two factors common to all the terms, 

= (a v . . . , a a -i) (a i+ i, ...,«„)[ (a a+ i, . . . , a P -i) (a p+ i, ...,««) (a^, . . . , a v _i) (« y +i, • • • , «s-i) 

- (a a+ i, . . . , a Y _i) (fly+i, . . . , a„) (a ls . . . , a P -i) (a p+h . .., a S -i) 
+ (a a+1 , . . . , a s _i) (a x , . . . , fl^-i) (ap+i, . . . , a v _i) (a y+1 , . . . , a«)] . 

Again, the last two terms inside the rectangular brackets here have two factors in 
common, their aggregate thus being 

= («i, . . . , a^_i) (a y+ i, . . . , an) { - {a a+h . . . , a y _i) (a p+1 , ...,a S -i)+ (a a +i, . - . , a«-i) (a p +i, . . . , « v -i)} , 

which, by an extension of the general theorem used in § 2 

= (a„ . . . , o^.!) (a y+1 , ...,«„)• (_ l)y-P+i (a a+1 , . . . , a^-i) (a y +i, . . . , a S -i); 



214 DR THOMAS MUIR ON 

and as this has two factors in common with the first term inside the rectangular 
brackets, the original expression takes the form 

• {(flfc+i, . . . , a n ) (a v . . . , a y _i) + (- lJr-P+ifa, . . ., a p -i) (a y+1 , .... On)} . 
Making a second use of the above-mentioned general theorem we can substitute 

(a v . . . , a„) (ap+i, . . . , a y _i) 

for the expression inside the double-curved brackets. The original expression is thus 
resolved into six factors, one of which is K, and the others 

('<!, • • • , Oa-l), (fflo+1, • • • , «0-l), ( a P + h • • • , a y-l)) («y+l. ■ • • , «S-l), («8-»-l, • . . , «n) , 

the product of which, from §§ 4, 5, we know to be 

cof a a apa y a$ . 

(13) The next auxiliary theorem used in § 9 is that which affirms that 

(a,h) (c,d) - abed + a(b,c)d = (a,b,c,d) * 
and 

(a,b) (c,d,ej) - abc(d,e,f) + a(b,e)d(e,f) - a(b,c,d)ef + a(b,c,d,e)f = (a,b,c,d,e,f) ; 
or that 

cof ab . cof cd - coiae.coibd + cof ad. cof be = (a,b,c,d) 
and 

cof ab . cof cdef 

- cof ae . cof bdef 
+ cof ad . cof beef } — (a,b,c,d,e,f) , 

- cof ae . cof bed/ 
+ cof of .coibede 



The general theorem which includes these concerns (a 1} a 2 , . . . , a 2n ), and is 

= (QSj, a 2> . . . , &.,„) j 



cof fljOSg . cof « 3 « 4 a 5 . . . ffljn 
- cof ajGfg . cof a 2 a A a r) . . . a 2 „ 
+ cof a l a i . cof a 2 a 3 a 6 . . . a. lH 



and there is a corresponding theorem for the case where the number of elements is odd, 
viz., 

cof a x a 2 . cof a 3 a 4 a 5 . . . a. 2 „ +1 \ 
- cof a^g . cof a 2 a 4 a 5 . . . a 2re+1 I = (« 3) a 4 , . . . , a 2re+1 ) . 



+ 



I 



(14) The two theorems may therefore be enunciated together thus : — 

If cof x denote the cof actor of x in the continuant K (a u a 2 ,..., a n ), then 

2,(- 1) T cof a x a r . cof a x a 2 . . . aja x a r = K , 

or = cof a x a 2 , 
■according as n is even or odd. 

* It should be noted that this is also a case of theirs* auxiliary theorem. 



THE DIFFERENTIATION OF A CONTINUANT. 215 

By way of proof we note that the first of the n— 1 terms on the left is 

(«1> a i) («3» a 4> • • • > «») » 

and that therefore we may write instead of it, 

K — a^a^ . . . , a„). 

Then, as the second of the n — 1 terms is 

- a x a 2 a 3 {a v ..., a n ) 
the aggregate of the first two is 

K - a x (a 2 , a 3 ) (a 4 , . . . , a„) . 

Similarly, the third term having the factor (a 2 , a 3 ) in common with this aggregate, the 
aggregate of the first three is found to be 

K - a x (a 2 , a 3 ) (a 6 , . . . , a n ) . 

This process being continued it is seen that the aggregates of odd numbers of terms- 
follow one law, and the aggregates of even numbers another law, viz., 

Terms. Aggregate. ȣ*_ Aggregate. 

I K - a x (a it .... a n ) , 2 K - a^(a 21 a 3 ) (a 4 , . . . , a„) , 

3 K - a t (a 2 , a 3 ) (o 6 , . . . , a„) , 4 K - a^, ...,a 5 ) (a 6 , . . . , a„) , 

5 K - a^, . . . , a 5 ) (a 8 , . . . , a n ) , 6 K - aj(a 2 , . . . , a 7 ) (a s , . . . , a„) , 

From the first column we learn that when n is odd the aggregate of the n—X 

terms is 

K - ^(og, ...,«„) 
i.e., (a 3) . . . , a„) , 
as was to be proved. 

Also, from the second column it is seen that when n is even the aggregate of n — 2 

terms (i.e., all the terms except the last) is 

K - a u (a,, . . . , a„_i) a n 

to which if we add the last, viz., + a x (a 2 , . . . , a n _^) a n , we obtain the aggregate 

K 
as desired. 

(15) There is however a more elementary theorem which leads easily up to this, 
and which can be more readily proved in the same way. It has to be noted too, that 
from some points of view it is of greater interest than that to which it leads. It is : — 

If 'cof a r stand for the cofactor ofa r in the continuant K(a,, a 2 , . . . , a n ), then 
a l cof flj - a. 2 cof a 2 + a 3 cof a 3 - . . . = K or 
according as n is odd or even. i 

To condense the proof we may take advantage of the fact that (oj, ...,«„) = 
(a n , . . . , a x ), and sum the half of the terms from the beginning and the half from the 
end. Thus, when n is even, equal to 2m, the aggregate of the first m terms is found 
to be 

K - (oj, . . . , a m ) (a m+l , . . . , a 2m ) or K - (a 1} . . . , a m _^) (a m+ .,, . . . , a 2m ) , 



216 DR THOMAS MUIR ON 

according as m is even or odd : and therefore the aggregate of the last m terms is 

- K + (a„„, . . . , a m+l ) (a„„ . . . , a 2 ) or - K + (a 2m , . . . , a m+2 ) {a m _ v ...,%) 

according as m is even or odd : from which we see that in either case the gross aggregate 
is 0, as was to be proved. 

Instead of using the cofactor notation ' cof ' we might have taken a hint from a usage 
in the exposition of the theory of general determinants, viz., where the cofactor of a rs in 
j Oi„ | is denoted by A rs . Our theorem would then stand thus : — 

If&i, a 2 , . . . , a n be the elements of a simple continuant K, and A l9 A 2 , . . . , A n their 
respective cojactors, then 

a^ - a. 2 A 2 + a 3 A 3 - . . . = K or 

according as n is odd or even. 

Without any notation for cofactors at all, it may however be neatly written as follows : — 

«1 («2» «3> • • • > a n) 
~ «2 ( a 3» • • • . a ») a l 

+ a. A (a 4 , . . . , a n ) (a v a. 2 ) 
- a 4 (o 6> . . . , a„) (a v a 2 , a 3 ) 



( - ^-^(a^gOg a n _ x ) = (a v a. 2 , . . . , a H ) or , 

the seemingly cyclical permutation of the elements arising from the act of reversing the 
order of the two parts of each cofactor. 

It is when stated in this last form that its suitableness for proving the theorem of 
§ 13 is most readily recognised. Thus, to take the second instance there given, we have 

(a, b) (c,d,e,f) - abc(d,e,f) + a(b,c)d(e,f) - a(b,c,d)ef + a(b,c,d,e)f 
= (c,d,e,f) - a{ b(c,d,e,f) 

- c(d,e,f)b 
+ d(e,f)(b,c) 
-e(f)(b,c,d) 
+f(b,e,d,e) } , 
= (?,d,e,f) + a(b,c,d,e,f) , 
= (a,b,c,d,e,f) . 

(16) The next point to be noticed is the effect of changing (a,b) into ab, (b,c) into 
be, or (c,d) into cd in the identity 

| (a,b) ac ad = (a,b,c,d). 
(b,c) bd 
(c,d) 

Such a change is clearly equivalent to subtracting (c,d), ad, or (a,b), — and therefore the 
right-hand side must be simultaneously changed into 

a(b,c,d), 
(a,b)(c,d), 
or (a,b,c)d . 



THE DIFFERENTIATION OF A CONTINUANT. 



217 



(17) We are now prepared to show that 

I (a, b) ac ad ae af = (a,b,c,d,e,f) , 

(b,c) bd be bf 

(e,d) ce cf 

(d,e) df 

M 

For, expanding the Pfaffian in terms of the elements of the first frame-] ine and their 
complementary minors, we have 



(a, b) | (c,d) ce cf 
(d,e) df 

fe/) 



- ac I bd, be, bf 

(d,e) df 
(e,f) 

- ae I (b,c) bd bf 

(c,d) cf 
df 



+ ad I (b,c) be bf 
I ce cf 

(e,f) 

+ af I (b,c) bd be 
(c,d) ce 
(d,e) 



which by § 16 is equal to 

(a,b) (c,d,e,f) - ac . b(d,e,f) + ad . (b,c) (e,f) - ae . (b,c,d)f + af(b,c,d,e) , 

and therefore by § 1 4 equal to 

(a,b,c,d,e,f) . 

(18) The effect of changing (a,b) into ab on the left of the preceding identity is 

to subtract 

\(c,d) ce cf i.e., (c,d,e,f) , 
I (d,e) df 

M 

and as the right-hand side equals 

a(b,c,d,e,f) + (c,d,e,f), 
the result is 

a(b,c,d,e,f) . 

The other changes taken in order lead to 

(a,b) (c,d,e,f) , 

(a,b,c) (d,e,f) , 

(a,b,c,d) (e,f) , 

(a,b,c,d,e)f. 



(19) In this way we reach the perfectly general theorem ^ 



(a v a 2 ) a x a s a x a 4 

(« 2 , « 3 ) a 2 a 4 • 
(a,, a 4 ) . 



i In 

a 2 a in 



— (a v a. 2 , . . . . , a^n) , 



( a 2n-l) a 2n) 

with which is connected the series of identities resulting from the change of any one of 

* It is worth noting that the elements of the Pfaffian are the two-line coaxial minors of the equivalent continuant. 
VOL. XL. PART I. (NO. 11). 2 K 



218 



DR THOMAS MUIR ON 



the hypotenuse elements from (a r , a r+1 ) into a r a r+1 , the corresponding change on the 



right-hand being from (a ls a 2 , 



. . , Oz r , cx> r +i, • • • , cc 2n ) into 

(«H «2 a ') K+l> • ■ • > a 2n) • 



(20) Now as the Law of Complementaries holds in regard to Pfaffians as well as in 
regard to determinants, let us apply it to find the Complementary of the general 
theorem just reached. Instead of each element of the Pfaffian we have to substitute its 
complementary minor ; and as the value of the Pfaffian is (a 1( a 2) . . . , a 2n ) the com- 
plementary minor of any element is nothing else than its cofactor in (a 1; a 2 , • • • » a 2n)- 
On the right-hand side the complementary minor of (a 1} a 2 , . . . , a 2n ) is 1, and therefore 
we have to annex to it a power of (a 1} a 2 , . . . , a 2n ) of the same degree as the altered 
Pfaffian on the left, viz., the degree n (2n — 2). 

I cof (a v a 2 ) cof a x a z cof a 1 a i . . . 

cof (a 2 , a 3 ) cof a 2 a 4 . . . 

cof (a 3 , a 4 ) ... 



We thus have the theorem 

= (ftj, Cl 2 , . . . , Ctzn) 



cof a^™ 
cof a 2 a 2 „ 
cof ct 3 a., n 



cof (a 2n _ u a 2n ) 

which is the generalisation surmised in § 10 to exist by reason of the two cases 
established in § 9. 

(21) Now, however, that we have accomplished the purpose with which we started, 
it is important to notice that the fundamental theorem of the whole is that given in 
§19. Any other mode of establishing it is thus of interest; and the known quanti- 
tative relation between Pfaffians and determinants suggests that by substituting 
determinants for squares of Pfaffians, the theorem in determinants thus resulting may 
be easy of proof, — in other words, that instead of proving, for example, that 



(a,b) 



ac 
(b,c) 



ad 

bd 
(c,d) 



= (a,b,c,d), 



we may seek to prove the identity resulting from this by squaring both sides, viz., the 

identity 

(a,b) ac ad a 1 

-(a,b) . (b,c) bd -1 b 1 

- ac - (b,c) . (c,d) . - 1 c 1 

-ad bd - (c,d) . - 1 d 



(22) Beginning then on the left-hand side, but taking a determinant of higher order 
so as to leave no doubt of the generality of the process, viz., the determinant 





(a,b) 


ac 


ad 


ae 


«/ 


-(a,b) 




(^c) 


bd 


be 


¥ 


- ac 


- (^) 




(c,d) 


ce 


cf 


— ad 


- bd 


-(c,d) 




(d,e) 


df 


- ae 


- be 


- ce 


-(d,e) 


■ 


(e,f) 


- of 


- ¥ 


- '■/ 


- 'V 


-(*,/) 


. 



THE DIFFERENTIATION OF A CONTINUANT. 



219> 



let us first perform on it the operations 






(row)! - *(row) 2 , 
(row) 2 _ -(row),, 



(row) 5 - - (row) fi , 



and then, to preserve the skewness, the corresponding operations 



(COI)! - -(C0l) 2 , 

(col) 2 - - (col) 3 , 



(col) 5 - - (col) 6 . 
The result of this is a zero-axial skew determinant which is the square of 



{a,b,c) 


a 






c 


b 




' 




(b,c,d) 


b 






d 


c 








(c,d,e) 


c 






e 


d 
(d,e,f) 



f 



- £ 

e 
1 



Developing the Pfaffian in terms of the elements of the first frame-line and their 
complementary minors, we see that it 

_ (a,b,c) j (c,d,e) , ,, c I a b (e,f) 
~ ~^~{ e " KJ) el b"c' T 

= (3M.( Ci d A f) - a -(e,f) 



= (a,b,c,d,e,f) 



as was to be proved. 



(23) If, on the other hand, we begin with (a, b, c, d, e,f) 2 we must try to trans- 
form its equal factors in such a way that the subsequent application of the multiplica- 
tion-theorem may produce the left-hand member. 

"Writing the factors in the form 



a 


1 












1 


- a 








. 


-1 


b 
-1 


1 

c 

-1 


1 

d 

-1 


1 

e 
-1 


1 
/ 


> 


h 
-1 


1 


1 

d 

-1 


-1 

- c 
1 


1 
/ 


-1 
— e 

1 



220 DR THOMAS MUIR ON THE DIFFERENTIATION OF A CONTINUANT. 

the second being got from the first by changing the signs of the 1st, 3rd, 5th columns 
and then exchanging the latter with the 2nd, 4th, 6th columns respectively, we find 
the product to be 



/ 
ef+1 



This is zero-axial skew, and a fair approximation to the form required ; but the further 
changes necessary are too many in number to be worth noting. 





at> + 1 


— a 






-ab-1 




2 


d 


-1 


a 


-2 




cd+\ 


- c 




-d 


-cd-l 




2 




1 


c 


-2 

-/ 


-e/- 



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TRANSACTIONS 



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VOL. XL. PART II.— FOR THE SESSION 1901-2. 



CONTENTS. 

XII. Ice-Erosion in the Cuillin Hills, Skye. By Alfred Harker, M.A., F.G.S. (With a 
Map), .......... 

(Issued separately 26th August 1901.) 



XIII. The General Form of the Involutive 1-1 Quadric Transformation in a Plane. 
Charles Tweedie, M.A., B.Sc, ... . 

(Issued separately 26th October 1901.) 



By 



XIV. Apparatus for Measuring Strain and Applying Stress ; with an Account of some Experi- 
ments on the Behaviour of Iron and Steel under Stress. By E. G. Coker, D.Sc. 
(With Eight Plates), ......... 

(Issued separately 12th November 1901.) 

XV. On the Anatomy of a Collection of Slugs from N. W. Borneo ; with a List of Species 
recorded from that Region. By Walter E. Collinge, Lecturer on Zoology and 
Comparative Anatomy in the University of Birmingham. (With Three Plates), 
(Issued separately 16th December 1901.) 

XVI. The True Shape, Relations, and Structure of the Alimentary Viscera of the Porpoise 
(Phoccena communis), as displayed by the Formal Method. By David Hepburn, 
M.D., F.R.S.E., and David Waterston, M A., M.D., F.R.S.E. (With Three Plates), 
(Issued separately 25th February 1902.) 

XVII. On the Primary Structure of certain Palceozoic Stems with the Dadoxylon Type of Wood. 
By D. H. Scott, M.A., Ph.D., F.R.S. (With Six Plates), .... 
(Issued separately 7th April 1902.) 

XVIII. On a Posdble Stridulating Organ in the Mosquito. (Anopheles maculipennis, Meig.) By 
A. E. Shipley, M.A., and Edwin Wilson, F.E.S. (With a Plate), . 
(Issued separately 21fih April 1902.) 

XIX. The Early Development of Cribrella oculata (Forbes), with Remarks on Echinoderm 
Development. By Arthur T. Masterman, M.A., D.Sc., F.R.S.E. (With Five Plates), 
(Issued separately 27th May 1902.) 

XX. A Bathymetrical and Geological Study of the Lakes of Snowdonia and Eastern Car- 
narvonshire. By T. J. Jehu, M.B., B.Sc. (Edin.), M.A. (Camb.), F.G.S. (With 
Eight Plates), ......... 

(Issued separately 16th June 1902.) 



&*. 






v^v 




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253 



263 



295 



313 



331 



367 



373 



419 



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( 221 ) 



XII. — Ice-Erosion in the Cuillin Hills, Skye. By Alfred Harker, M.A., F.G.S., 
Fellow of St John's College, Cambridge; H.M. Geological Survey of Scotland. 
Communicated by John Horne, F.R.S. (With a Map.) 

(Read 20th May 1901.) 



I. General Account of the Glaciation 

of Central Skye 221 

(i.) Introduction 221 

(ii.) Independent Ice-Cap of the Skye 

Mountains 222 

(iii.) Movement of Ice during the Great 

Glaciation 225 

II. Physical Features of the Cuillin Hills as 

a typical district of Ice-Erosion . . 227 
(iv.) General Considerations . . . 227 
(v.) Independence of Physical Features and 

Geological Structure . . . 230 



page. 



(vi.) Forms of the Valleys, and Relation of 

Tributaries to Principal Streams 
(vii.) Cirques : Character of the Ridges 
(viii.) Longitudinal Profile of Valleys : Lake- 
Basins ...... 

(ix.) Asymmetric Element in the Surface- 
Relief 

III. The Glacial Accumulations and 
their testimony to ice- and frost- 

Erosion 

(x.) Drift Deposits . . . . .242 
(xi.) Later Glaciers and Frost-Erosion . . 248 



231 
234 

237 

240 



242 



I. General Account of the Glaciation of Central Skye. 

(i.) Introduction. 

Since the publication in 1846 of a brief but valuable memoir by J. D. Forbes, in 
which that author drew attention to " the traces of ancient glaciers " in the Cuillin 
Hills, that district has remained almost unnoticed by glacial geologists for half a 
century.* This neglect is doubtless attributable chiefly to the difficulty of access to 
the mountains, a consequence of their peculiar configuration, which in turn is closely 
bound up with the glacial history of the district. The present contribution is the 
outcome of observations made during the years 1895-1900 in mapping the central 
part of Skye for the Geological Survey of Scotland.! In traversing the mountains 
day after day throughout several successive seasons, the writer has been struck 
especially by the impressive evidence which they present of glacial erosion as the 
dominant factor in their sculpture, and to enforce this is the chief object of the present 
communication. 



* J. D. Forbes, " Notes on the Topography and Geology of the Cuchullin Hills in Skye, and on the Traces of 
Ancient Glaciers which they Present," Edin. New Phil. Joum., vol. xl. pp. 76-99, pi. iv., v., 1846. Among scattered 
notices of later date, see A. Geikie, " On the Phenomena of the Glacial Drift of Scotland," Trans. Geol. Soc. Glasg. y 
vol. i. part ii., 1863 ; and J. Geikie, The Great Ice Age ; also for the adjacent Red Hills, T. G. Bonney, "On a 
Circme in the Syenite Hills of Skye," Geol. Mag. 1871, pp. 535-540. 

+ Some of these observations have been briefly recorded in the Summary of Progress for 1897 and 1898. See 
also Harker, " Glaciated Valleys in the Cuillins, Skye," Geol. Mag. 1899, pp. 196-199. In the following pages the 
subject is developed more fully than would be convenient in an official publication. 

VOL. XL. PART II. (NO. 12). 2 L 



222 MR ALFRED HARKER ON 

Concerning the general orography and ' solid ' geology of central Skye a few words 
will suffice in this place. The Cuillins are built essentially of a great laccolitic mass of 
gabbro, enclosing patches of metamorphosed basaltic lavas and traversed by countless 
dykes and sheets also of basic rocks. The main range, rising in many places more 
than 3000 feet, has roughly the form of a semicircular arc, with its concavity to the 
east. A lower branch ridge (Druim nan Ramh, etc.) runs S.E., enclosing the 
basin of Coruisk with outlet south-eastward to the sea-loch Scavaig. Further east is 
the Rlath-bheinn range, running nearly N. to S., which is also of gabbro, but is cut off 
by Strath na Creitheach, which drains southward by Camasunary. The interior of the 
northern Cuillins is drained by the Sligachan River,, which turns northward and finds 
an outlet in the sea-loch Sligachan. East of Glen Sligachan is a range of hills 
composed of granite and granophyre, the beginning of a tract of like rocks which 
extends nearly to Broadford. These ' Red Hills ' are almost always less than 2500 feet 
in altitude, and they have smooth rounded forms which contrast very markedly with 
the bold peaks and acute ridge-lines of the Cuillins. Outside the two mountain-groups, 
the central portion of Skye is built essentially of basalt, in the form of greatly eroded 
plateaux rarely rising more than 1500 feet above sea-level. The older stratified rocks 
(Torridonian and Jurassic), upon which these basalts rest, are exposed only in places 
along the coast. The coast-line is highly irregular in outline, long sea-lochs running 
up in some places almost or quite to the base of the mountains. 

It is greatly to be regretted that we have as yet no satisfactory map of the 
Cuillins, the more so since what here follows deals in great part with the detailed 
topography of the district. An accurate and carefully contoured map of this the finest 
of all the mountain-groups of Britain would be eminently interesting to the physical 
geographer. The original Ordnance Survey* was made at a time when much of the 
mountain district was considered inaccessible ; and, although later issues embody 
numerous corrections, they still leave much to be desired. Contour-lines are drawn 
on the one-inch map only, and they cannot pretend to more than approximate 
accuracy. 



(ii.) Independent Ice-Cap of the Skye Mountains. 

We proceed to a general view of the glaciation of the Cuillins and adjacent country, 
as preparatory to a closer consideration of our special subject. What at once challenges 
interest is the fact that the Skye mountains, at the stage of maximum glaciation, 
sustained a small local ice-cap, round which the great Scottish ice-sheet flowed on 

* The maps illustrating the present paper are, Scotland (one-inch), sheets 70 and 71 ; Skye (six-inch), sheets 38, 39, 
44, 45, 49, and 50. A reduced copy of the six-inch map of the Cuillins, with additional names and heights, is given 
in No. 25 of the Scottish Mountaineering Club Journal, issued January 1898. For some corrections of the toj>ography 
of the ridges, see a rough sketch map by C. Pilkington, pub. 1890 (Manchester) ; also W. Douglas, S.M.G.J., vol. 
iv. pp. 209-213, 1897 ; and A. Harkkr, ibid., vol. vi. pp. 1-13, 1900. 



ICE-EROSION IN THE CUILLIN HILLS, SKYE. 



22JT- 



both sides. That the glaciation of this part of the island was strictly local, has been 
recognised by other observers, e.g. by Professor Jas. Geikie. # The relations are 
roughly exhibited upon the small sketch map (fig. 1), where the movement of the 
Scottish ice in south-eastern Skye and on the neighbouring mainland is laid down from 
information kindly communicated by my colleague Mr C. T. Clotjgh, while data con- 
cerning the north-eastern part of the area are afforded by the published sheet 81 of 
the Geological Map of Scotland. The south-eastern portion of the island, which includes 




Fig. 1. — Sketch map to show the relation of the Skye ice-cap to the Scottish ice-sheet. The heavy line indicates approxi- 
mately the boundary between the native and foreign ice at the stage of maximum glaciation. The arrows give 
the direction of movement. The rectangular area marked out is that included in the detailed map below. [The 
latter has subsequently been extended a little farther, both eastward and westward.] 



few considerable elevations, was completely overridden by ice from the mainland of 
Scotland ; but the ice generated upon the Cuillins and the Red Hills was always 
powerful enough to defend its own small territory against the Scottish invasion."*" Of 
this we have ample proof both in the direction of the glacial striae and in the absence 

* " The lofty Coolin Mountains of Skye .... formed of themselves a centre of dispersion, but the northern 
parts of the island were overflowed by the ice that crent out from the great glens of Ross." — The Great Ice Aye, 
p. 83 of third edition, 1894. 

t It would perhaps be more accurate to say that if, at an early stage, the Scottish ice did obtain a footing among 
the Skye mountains, it has left absolutely no trace of its occupation ; and the episode, if it ever occurred, is not to 
be reckoned with as a factor in the glaciation of the area as it is now to be studied. 



224 MR ALFRED HARKER ON 

of foreign boulders from the area. The exceptions to this latter generalisation are of 
a kind which go to emphasize the rule. Boulders of rocks foreign to the district 
(which farther S.E. occur at all altitudes) are found in central Skye only near the 
shore ; usually about high- water mark, but occasionally up to 50 or even 75 feet above 
sea-level. It is to be noted that occasional relics of the ' hundred foot ' raised beach 
prove that the land stood lower by that amount about the close of the glacial period. 
Since these foreign erratics are never embedded in the boulder-clay, but lie exposed 
on the surface, there is no difficulty in supposing that they have been transported by 
floating ice at a late stage of the Glacial period.* 

Both the Cuillins and the Eed Hills afforded gathering-ground for the ice. The 
latter, though less lofty, are not less extensive than the former ; and it appears from 
the thick accumulations of drift on the edge of the granite tract, and from the wide 
dispersal of granite boulders, that this group of hills played, in some respects, almost 
as important a part as the other. The nature of the granite of the Eed Hills, however, 
does not lend itself to the preservation of glacial scorings, while the generally uniform 
character of the rock makes it impossible to trace the movement of the ice in detail 
by the distribution of boulders. For these and other reasons it is much less easy to 
obtain precise data in the Red Hills than in the Cuillins with their adjacent basaltic 
tract, and it is to these latter that we shall confine our attention. It is not to be 
understood that the Cuillins and the Red Hills were in any sense two distinct centres 
of glaciation. They formed together a single gathering-ground about 12 miles long 
in an E. to W. direction, with a breadth of 5 or 6 miles and an area of roughly 
40 square miles. 

During the maximum glaciation the central part of Skye was not merely a 
feeding-ground for glaciers : it carried a true ice-cap, under which the mountains 
were wholly buried. The evidence of this is cumulative, and is implicitly involved 
in much of what follows. We may note in this place, however, that such a conclusion 
appears inevitable from the consideration that the local ice was able to withstand the 
pressure of the ice-sheet from the mainland. It is certain that throughout a long- 
time the two were in equilibrium along their line of confluence, indicated approximately 
in the small sketch map (fig. 1). Here the thickness of the Skye ice must have been 
equal to that of the Scottish, i.e., probably not less than 3000 feet. A very moderate 
rate of rise from here towards the mountains would suffice to carry the surface well 
above the highest summits. The ice was presumably thickest over the broad double 
strath which divides the Cuillins on the west from Blath-bheinn and the Red Hills on 
the east, and is formed by the lower portions of the Camasunary and Sligachan valleys, 
the one running south and the other north. The watershed dividing these two valleys 

* This remark applies to the occasional boulders, some of large size, found in places along and above the sea- 
lochs. Where the present coast-line lies near what was the boundary of the Scottish ice, as in many places between 
Bioadford and Loch Ainort, we find on the beach more numerous fragments of foreign rocks, doubtless washed out 
of the ground-moraine of the Scottish ice-sheet. 



ICE-EROSION IN THE CUILLIN HILLS, SKYE. 225 

is only 250 feet above sea-level, and over this point we may conceive the summit of 
the ice-cap to have been situated. Some such supposition is necessary to account for 
the enormous volume of what we may style the interior ice-drainage of the Cuillin 
district. The ice-streams which found outlet by the three principal interior valleys 
already mentioned — viz., Coruisk, Camasunary, and Sligachan — were clearly of far 
greater volume than those which drained the exterior valleys of the Cuillins. The 
Sligachan ice-stream, for instance (see map below), on emerging from its valley, 
spread out fan-like through an angle of at least 120°, crossing several minor watersheds 
and over-riding the hills (sometimes 1300 or 1400 feet high) as well as the lower 
ground. Its left wing swept round the northern end of the Cuillins into the head of 
Glen Brittle, penning into the narrow space between there and the mountains the ice 
from all the northern and north-western corries. Its right wing, moving northward, was 
for some distance strong enough to prevent the Scottish ice (with that from the eastern 
Red Hills) from encroaching upon the coast of Skye. All this bespeaks a very great 
thickness farther back, in the comparatively restricted valley and on the central water- 
shed. Other features in the movement of the ice of the Cuillins point to the same 
conclusion, and we shall see that the boulders in the drift accumulations afford strong 
confirmatory evidence. 



(iii.) Movement of Ice during the Great Glaciation. 

The movement of the ice in and immediately around the Cuillins during the stage 
of maximum glaciation is sufficiently indicated on the large map below. The chief 
data are the directions of striae on rock surfaces and the distribution of boulders 
of recognisable rock- types. These two criteria supplement one another, the former 
being of most service among the mountains and the latter on the lower ground ; 
while various other circumstances, such as the moulding of exposed crags, afford 
additional information. The striae necessarily give the direction of movement of the 
lower layers of the ice only, and we shall see that this is also true in great measure of 
the dispersal of boulders. 

It is seen that within the mountain area proper, the natural outward flow was, in 
general, closely guided, as regards the lower layers of the ice, by the form of the 
ground. The main ridge-line of the Cuillins and the higher parts of the principal 
branch ridges everywhere acted, for these lower layers, as an ice-shed. Some of the 
branch ridges, however, were over-ridden. The most striking example of this is 
afforded by the ice from Lota Corrie and the upper part of Harta Corrie. These form 
the interior basin of the northern Cuillins, and now supply the head-waters of the 
Sligachan River, which turns through a complete semicircle before running northward 
to Sligachan. The ice-drainage took a more direct line, and found an outlet southward, 
a large part of it crossing obliquely the ridge of Druim nan Ramh into the Coruisk 



226 MR ALFRED HARKER ON 

basin. In following this course part of the lower layers of the ice would have to face 
an upward gradient of about 1 in 4 for a distance of nearly three-quarters of a mile. 
Such behaviour would be incomprehensible in a valley glacier, but it is intelligible on 
the supposition that the Sligachan valley near Loch Dubh watershed was occupied by 
ice extending higher than the summits of the Cuillins. 

Immediately outside the mountain area proper, a new and potent factor came 
into play, viz., the pressure of the Scottish ice-sheet coming from the east. Hence we 
find a sharp westward diversion of the great ice-streams from the Sligachan, Cama- 
suuary, and Coruisk valleys and of the other branches, such as that from the east side 
of Blath-bheinn. The interior ice-drainage in turn bore back that from the outer side 
of the Cuillins, as alread}^ remarked, so that, with increasing distance from its source, 
the movement of the native ice conformed more and more to that of the great Scottish 
ice-sheet. In the Red Hills the relations must have been more peculiar, for there 
some important valleys opened directly upon the flank of the invading Scottish ice. 
It is probable that at the climax of glaciation no point in the Isle of Skye rose above 
the ice. It is certain, at least, that for many miles from the Cuillins hill and valley 
were alike buried, and the form of the ground exerted only a very partial control over 
the direction of flow. The mid-stream line of the ice from Grlen Sligachan crossed three 
watersheds in its nearly semicircular course from Sligachan to Loch Eynort ; while the 
left wing of the same ice-stream found its way over the pass Bealach a' Mhaim, to the 
north of Bruach na Frithe, part of the base of the stream rising for this purpose about 
1000 feet in a distance of three miles. 

As already remarked, the direct evidence concerning the direction of flow of the 
ice is applicable to the lower portion only. It is not improbable that the upper layers 
followed in some places a somewhat different course. In the mountain area their 
movement would be less directly influenced by the configuration of the land-surface, and 
might more nearly realise the ideal radial outflow. Elsewhere the direction of move- 
ment might cross a valley occupied by ice either stagnant or flowing down the valley. 
There is reason to believe that something of this kind occurred at one time in the case 
of Loch Sligachan. Since in discussing glacial erosion we are concerned with the basal 
portion of the ice only, it is not necessary to pursue this question. 

The foregoing account concerns the principal glaciation of the area only. Here, as 
in some other parts of Britain, there was a later and minor glaciation, taking the form, 
not of an ice-cap, but of glaciers occupying the valleys. At this stage the obstruction 
offered by the Scottish ice-sheet had been removed, and the Skye ice was free to follow 
a course more in accordance with the local topography, as is partly shown by the second 1 
set of arrows on the map. 



ICE-EROSION IN THE CUILLIN HILLS, SKYE. 227 



II. Physical Features of the Cuillin Hills as a typical district of 

Ice-Erosion. 

(iv.) General Considerations. 

Viewing ice-work in its dual aspect — destructive and constructive — we may expect 
to find beneath an independent ice-cap, an inner area of glacial erosion and an outer 
area of glacial accumulation. Allowing for a broad intermediate belt, in which the two 
processes have operated either successively or simultaneously side by side, we may 
recognise an approximate partition of this kind in the central part of Skye. The 
presence of ice-worn and striated surfaces does indeed show that no part of the area 
surveyed was quite beyond the province of glacial erosion ; but with increasing distance 
from the mountains these signs become less frequent, while the mantle of drift becomes 
more persistent and uniform. In the mountain district itself, on the other hand, the 
drift disappears, and the evidence of important glacial erosion is displayed in the most- 
striking manner. In this generalised statement, and still more in the detailed features 
to be described, we have a further confirmation of our supposition that the ice attained 
its greatest thickness over the mountain area proper. It cannot be doubted that, other 
conditions being the same, erosion would be most active at places where the pressure at 
the base of the ice was greatest, and the pressure at different places would bear approxi- 
mately a direct ratio to the thickness of the ice. 

In discussing the phenomena of glacial erosion it is, then, to the Cuillins that we 
must turn as the principal theatre of operations. Several causes contribute to make 
this group of mountains a model of a well-marked type of glaciated topography. 
Highly complex as it is in detailed structure, it may be broadly regarded as carved out 
of a single unbroken rock-mass — viz., a great laccolite of gabbro. Another element of 
simplicity arises from the independence of this centre of glaciation. The ground has 
not been over-ridden, as in some other districts, by a foreign ice-sheet crossing ridge 
and valley indifferently. The pre-Glacial surface-relief was strongly marked, and the 
movement of the ice was guided, with few exceptions, by the form of the ground, so 
that it exercised throughout the whole time a cumulative effect as regards developing 
the characteristic forms in their simplest expression. It is a further advantage that the 
actual shape of the ground is everywhere clearly exhibited. The mountains themselves 
are of perfectly naked rock ; the same is true of all the higher corries, except in so far 
as they are encumbered with screes ; and even in the lower corries and main valleys the 
drift is never so thick as to obscure the true form. Again, it is to be remarked that the 
effects of ice and frost-action remain practically without modification by later agencies, 
the sum total of post-Glacial erosion being almost a negligible quantity.* Finally, it is 

* See Harkee, "Notes on Subaerial Erosion in the Isle of Skye," Geol. Mag. 1899, pp. 485-491. 



S 



228 MR ALFRED HARKER ON 

essential to some of the considerations to be adduced below to note that the pre-Glacial 
drainage-system of Skye was a fully matured one. The igneous rocks are of Eocene age, 
and perhaps in part later, but the}^ had undergone an enormous amount of erosion 
during the latter half of Tertiary time, prior to the advent of the Glacial epoch. Bear- 
ing in mind that, under the conditions now existing, erosion is practically at a stand- 
still, it is difficult to resist the inference that during the carving out of the pre-Glacial. 
valleys the land stood somewhat higher than it does to-day. At the close of the 
glaciation it stood about 1 00 feet lower than at present. These and other considera- 
tions may suffice to assure us that at the time when glacial conditions were initiated the 
land had not experienced any recent elevation : the drainage-system was a fully 
established one, with valleys adapted to the streams which flowed in them and with the 
normal adjustment of tributaries to principal valleys. The point is of importance in 
comparing the types of topography due to ice- and water-erosion respectively, for some 
of the most instructive points of contrast do not hold good in their full degree unless 
this condition is realised. 

It is part of the plan of the present contribution to confine attention to the 
special phenomena of the selected area, which, as has been indicated, has peculiar 
claims to be regarded as a type, and accordingly few references will be made to 
other districts. Still less is it within our province to discuss in its generality the 
much-vexed question of the degree of importance to be attached to ice as an erosive 
agent. Having regard to the mechanical element in erosion only, it is manifest 
that a sand-grain gripped in the sole of a glacier, or of an ice-sheet thousands of feet 
in thickness, must be incomparably more efficient as a graving-tool than the same 
grain rolled along the bed of a stream. The question, therefore, from the a priori 
point of view, turns upon the rate of working and the duration of the requisite 
conditions. As regards the former point, it is to be observed that, where a groove 
lias been cut in a rock-surface by abrasion by an individual sand-grain dragged along 
it, the time required to cut the groove was obviously the time taken by the grain 
in travelling the length of the groove. Assigning even a low rate of flow to the 
ice, and allowing for the sand-grain lagging behind the ice in its movement, this 
consideration still suggests that the removal of material thus effected by ice well 
supplied with rock-debris in its lower layers must be a rapid process as compared 
with anything that can be effected by the agency of running water. The duration 
of the Ice Age is a question upon which we cannot enter in this place. 

It is beyond doubt that the carving out of the mountain and valley system of the 
Uuillins is, as regards its broad outlines, the result of aqueous erosion during the 
latter half of Tertiary time ; but it is no less certain that the actual details of the 
relief, as we now see them, are to be credited to the action of ice and frost during 
the Glacial period. If we have regard to the total amount of material removed, we 
must recognise water-erosion as the chief factor in the result ; but from the point of 
view of earth-sculpture it is to glacial erosion that we must assign the more important 



ICE-EROSION IN THE CUILLIN HILLS, SKYE. 229 

role. The latter agent, following upon the former, has replaced the forms character- 
istic of aqueous erosion by those proper to itself ; and it is in the peculiar topography 
thus developed that we find the most convincing proofs of the important part played 
by glacial erosion in this district. 

The most palpable evidence of the abrasive power of ice, fortified by included 
de'bris, is seen in the rounded, grooved, striated, and polished rock-surfaces throughout 
the gabbro mountains. Excluding only the higher parts of the summit-ridges, where 
this characteristic appearance has been obliterated by subsequent frost-weathering, it 
is scarcely too much to say that almost every square foot of the surface bears in this 
way the stamp of glaciation. Very striking are the shores of Loch na Creitheach and 
Loch Coruisk and the sea-loch Scavaig, localities known to many tourists ; but an 
equally remarkable display is seen on the floor of any of the higher corries or on a 
steep smooth mountain-slope such as the west faces of Blath-bheinn, Sgurr na Stri, 
and Druim nan Ramh. The same smoothing, fluting, and polishing is found on the 
vertical walls of gullies and on the undercut and overhanging rock-surfaces, which are 

o DO 7 

not uncommon in some parts of the Cuillins. It is clear that the ice has been in 
close contact, throughout its whole extent, with the subjacent rocks, and has forced 
its way into hollows and openings, vertically and horizontally, in a fashion which 
argues effective plasticity in its lower layers. The conditions were totally different 
from those which obtain beneath an Alpine glacier near its termination. 

In this connection it is instructive to turn from the mountains proper to the belt 
of country a little beyond them, where the ice has evidently had much less erosive 
power. Here we find that the bottoms of certain deep gorges have escaped glacial 
erosion. The best example is the gorge of Allt Coire na Banachdich, just below 
Eas M5r, where for some distance the gabbro is so rotten that it can be dug with a 
spade. Something similar is seen in the gorge of Allt a' Coire Ghreadaidh. These 
few places preserve the only relics in the district of the pre-G-lacial weathered surface. 

Another difference between the mountains and the bordering tract is seen in 
the form of the roches moutonnees. In the sub-montane belt these exhibit the well- 
known contrast between "Stossseite" and " Leeseite," but among the mountains each 
knoll and ridge is commonly as well rounded and polished on the lee as on the weather 
side. It is not to be supposed, however, that in the former case the craggy shape of 
the lee side is an indication that ice-erosion has not operated on it : only the mode 
of operation was different, taking the form of fracture instead of abrasion. This point 
will be considered later. 

The impression of a smooth rounded outline upon every prominence, implying as 
it does the removal of a considerable amount of material, is enough to show that the 
work of the ice was something more than a mere excoriation of the surface. It is very 
far, however, from affording a measure of the actual amount of glacial erosion. An 
idea of this is to be gained only by an analysis of the physical features of the 
mountain-district, distinguishing those due to glacial from those due to aqueous 

VOL. XL. PAET II. (NO. 12). 2 M 



230 MR ALFRED HARKER ON 

action. In the writer's opinion, such analysis is to a great extent practicable, and an 
essay towards it is offered in the following divisions of this section. The mechanics 
of ice in bulk presents in its entirety a difficult physical problem, as yet unsolved. 
It follows that we have no basis for a full a priori discussion of the mechanism of 
glacial erosion, and the attempts hitherto made on this line are necessarily inconclusive. 
M' Gee's investigation,* for example, involves in many parts conflicting elements, the 
relative magnitudes of which are not known. But although we have no working 
theory of ice-erosion, we have a theory of water-erosion which is complete in most 
essentials and is amply justified by the results to which it leads. It supplies us with 
most important laws built up on a few simple principles. These fundamental 
principles are proper to water but alien to ice, and this must be true of the con- 
sequences deduced from them. Thus, although it may be difficult to lay down a priori 
the laws of ice-erosion, it is not difficult to see in many cases how they must differ 
from the laws of water-erosion ; and different laws will find their expression in different 
topographic forms. This is the point of view to be adopted here. The differences in 
question fall conveniently under five heads. 



(v.) Independence of Physical Features and Geological Structure. 

A study of the actual topography of the Cuillins shows that, under the conditions 
that there prevailed, ice-erosion is controlled in a much less degree than water-erosion 
by lithological differences and geological structure. 

One consideration which would lead us to anticipate this difference is sufficiently 
evident ; while in the case of water-action the process is effected by the co-operation 
of chemical with mechanical disintegration, in ice-action the chemical factor is 
minimised or wholly in abeyance. We shall have to notice below, other circumstances 
which conduce to simplicity of form on glaciated land-surfaces, and so tend to overrule 
the expression of geological constitution in surface-relief. 

The general principle propounded is beautifully illustrated in the Cuillins. This 
group of mountains, remarkably simple in constitution in a broad view, is in detail 
highly complex. On the summit-ridges and on many parts of the higher slopes this 
complexity of structure expresses itself in the form of the ground. Many of the 
dykes give rise to gullies and notches, and the parallel intrusive sheets of dolerite 
impart something of a step-like character to the slopes. All this becomes most marked 
in those places which have suffered most from frost-weathering after the epoch of ice- 
moulding. On the floors of the corries, and in the main valleys, i.e. in places where 
the maximum effects of glacial erosion have been experienced and the resulting surface 
remains intact, the appearance is very different. Here we see gabbro, basaltic lavas, 

* W. J. M'Gke, "Glacial Canons," Joum. of Geol., vol. ii. pp. 350-304, 1894. 



ICE-EROSION IN THE CUILLIN HILLS, SKYE. 231 

dykes, and sheets eroded down to a common level and figuring upon a single smooth 
flat rock-surface. Throughout the interior of the mountain area indeed, all the 
conspicuous features—precipices, ridges, barriers, basins, etc. — are carved out of the 
rock-complex in a fashion wholly irrespective of lithological differences or geological 
structure. Only on the outskirts of the mountains do we find exceptions, which thus 
o-o to emphasize the rule. This is seen, for instance, on the southern face of Gars- 
bheinn, and still more clearly in the form of the corries to the east of that mountain 
(see Ordnance Map), where the juxtaposition of gabbro and basaltic lavas has given 
rise to some bold escarpments. Here, where glacial erosion has played a less dominant 
part in shaping the existing land-surface, geological structure has asserted itself in 
the usual mauner. 



(vi.) Forms of the Valleys, and Relation of Tributaries to Principal Streams. 

We may now proceed to recall some of the more obvious differences between ice 
and water which may be expected to aid us in discriminating the effects produced by 
these two agents of erosion. Running water in a valley concentrates its direct action in 
oreat part upon certain narrow channels, viz., the main stream and its tributaries. The 
courses of the tributaries, and even of the main stream in different parts of its course, 
make various angles with the general direction of the valley. If now we suppose the 
valley to become occupied by ice moving down it, the conditions are greatly changed. 
A glacier fills a large part of the width of the valley ; an ice-cap, as in the Cuillins at 
the principal glaciation, more than fills the whole valley. Moreover, we vatxy, as a first 
approximation to the truth, consider this body of ice as moving down-stream as a ivhole. 
The differential movement which takes place within the mass imports a considerable 
modification of this broad view, but does not destroy its validity for our argument : 
though ice is not a ' rigid ' substance, it is rigid in comparison with water. 

This different manner in which the eroding force is applied must produce results 
which can in part be foreseen. We must expect a tendency to simplification of the 
form of the valley in ground-plan and in cross-section (the longitudinal profile falls 
under other rules). Lateral erosion — unfettered here by any consideration of ' base 
level' — will come into play to reduce or destroy projecting spurs, to straighten curved 
reaches, to plane away the subsidiary ridges which separate adjacent minor tributaries, 
etc. ; and the result of such action, if continued, will be to widen the floor of the 
valley and to straighten and steepen its walls. 

The valleys of the Cuillins are straight in ground plan,* and this straightness 
extends also in very great measure to the slopes which bound them. Transversely 
they show a flattening of the floor and a steepness of the bounding walls, which give 

* Harta Corrie is the only exception, and here we have already seen that, at the maximum glaciation, the ice 
when it reached the curve no longer followed the direction of the valley. 



23i> 



MR ALFRED HARKER ON 



2050 



the characteristic canal-shaped or ' U-shaped ' cross-section (figs. 2 and 5) recognised 
in many other glaciated areas. The persistence of this form of cross-section along the 

middle and principal part of the valley's 
course, in conjunction with the straight - 
ness and smoothness of the sides, 
already adverted to, results in some- 
thing like a semi-cylindrical shape in 
this portion of the valley, when most 
typically developed. Since it is 
difficult to visualise the actual shape 
of a valley from a contoured map 
alone, a rough attempt is made in 
figs. 3 and 4 to render it in another 
fashion. The appearance as seen on 
the ground is quite marked. One may 
describe it roughly by saying that the valleys give the impression of trenching unduly 
upon the dividing ridges and being too large, and in particular too wide, for the district. 



S.W. 



N.E. 



Fig. 2. — Transverse section of the Coruisk valley about ^ mile 
above the head of the loch ; scale, about 2J inches to a mile. 
The horizontal line shows the sea-level (O.D. ). 

This and the other sections are drawn from the contoured 
Ordnance Map with the aid of additional altitudes taken 
with the aneroid. They are drawn to true scale as regards 
horizontal and vertical distances, but they cannot pretend to 
close accuracy in detail. [The original drawings have unfor- 
tunately been reduced on no settled scale.] 





Fig. 3. — Ground Plan of Coir' a' Ghrunnda. 



Fig. 4. — Ground Plan of Coire Labain. 



The lines in these two figures are not contour-lines of the ordinary kind. They are intended to show elevations, not 
above sea-level, but above the neighbouring floor of the valley ; thus eliminating the inclination of the valley-floor itself. 
The figures bring out well the form of the cirque in which any of these valleys heads, as described below. Of the two, 
Coir' a' Ghrunnda has a very elevated cirque and a semicylindrical middle course ; Coire Labain has a larger cirque at a 
somewhat lower level, and a rather more open valley below. Scale, about 3 inches to a mile. 

It remains to consider the tributary glens in their relation to the trunk valley to 
which they belong. In so far as the ice filling the latter moves as a solid body, it must 
tend to pond back the smaller tributary ice-streams, at least when these debouch in 
directions making high angles with the trend of the main valley. We must expect 



ICE-EROSION IN THE CUILLIN HILLS, SKYE. 233 

that this tendency will become effective in varying degree, depending inversely upon 
the magnitude of the tributaries. The smallest of these will be completely blocked ; 
the larger may be only partially checked, or at least they will surrender their freedom 
of exit later in the waxing stage of glaciation and recover it sooner in the waning stage ; 
the largest will be able to assert themselves throughout. For these reasons — apart from 
the consideration of the varying thickness of the ice as affecting the rate of erosive 
action — we must look for much more erosion in the main valley than in the smaller 
tributary glens. Moreover, while the bottom of one of these latter is occupied by ice 
which is not effectively eroding, the upper parts of its bounding slopes may be reduced 
by the action of ice moving athwart the direction of the glen. 

These points seem to be illustrated in the Cuillin district. In the first place the 
sides of the main valleys are formed in some cases by long straight mountain-slopes 
broken only by narrow gullies. The west face of Blath-bheinn and the south-west 
slope of Druim nan Ramh are good examples, in Strath na Creitheach and Coruisk 
respectively. The ice-worn surfaces inside these gullies prove that they are not of post- 
Glacial age ; and they seem to be the relics of larger glens which have been almost 
obliterated, just as an inscription cut in a stone slab is obliterated by grinding away the 
surface.* The walls of the gully never curve towards the wall of the main valley to 
form a continuous surface with it. The pre-Glacial glens in these places, though larger 
than the gullies which now represent them, were evidently of very small dimensions. 
They must have been wholly aborted as channels during the great glaciation. In this 
connection it is instructive to contrast the slope of Druim nan Ramh overlooking 
Coruisk with the opposite side of the same main valley. 

A different and very interesting case occurs where a tributary glen of larger 
dimensions than the preceding, but still small in comparison with the trunk valley, has 
come steeply down to join the trunk in a direction making a high angle with it. Here 
the lower part of the tributary glen may have been greatly reduced or wholly 
obliterated by the planing process, while its head has been on the other hand 
developed into a cirque in the manner to be discussed later. Of this, numerous 
examples, with various modifying circumstances, are found in the Cuillins, the most 
remarkable being Coir' an Lochain, overlooking Coruisk. Here we have a corrie 500 
yards across and going back 1000 yards, the tarn on the floor of the corrie being at an 
altitude of over 1800 feet. The stream draining this, on emerging from the corrie, 
plunges abruptly over a steep slope, fully 1000 feet high, consisting of smooth glaciated 
rocks in which there is, for the most part, no sort of channel. The strise which 
everywhere mark this steep slope, and may be seen through the water which 
cascades over it, axe parallel to the direction of Coruisk and at right angles to the 

* Something comparable with this has been described by Dr W. T. Blanford in the Great Glen of Scotland 
(" On a Particular Form of Surface, apparently the Result of Glacial Erosion, seen on Loch Lochy and Elsewhere," 
Quart. Joum. Geol. Soc, vol. lvi. pp. 198-203, pi. ix., 1900). There are. however, considerable differences between 
the two cases. 



234 MR ALFRED HARKER ON 

tributary stream itself. Higher up, however, we find the striae emerging from the 
corrie in the natural direction and then curving away into the direction of the Coruisk 
valley. In this case it seems impossible to doubt that there has been a considerable 
pre-Glacial valley, the lower half of which has been completely planed awa}?-. The 
Coir' an Lochain ice was too powerful a body to be ponded back, and it accordingly 
swept out to join the main stream ; but it did this at a high level, the lower part of 
the valley thus ceasing to operate as a channel and being thereupon gradually ground 
out of existence by the action of the Coruisk ice streaming directly across it. Only in 
this way can we explain the situation of this and other high-level niches in the 
Cuillins, though the amphitheatral form to which they so generally tend involves 
another element not yet considered. 

What has just been described as illustrated by Coir' an Lochain has much in 
common with what Davis,* following Gilbert, has termed ' hanging valleys.' 

These are simply tributary valleys which debouch at levels considerably above the 
floor of the trunk valley, into which they therefore drain by cascades of some height. 
They seem to be a characteristic feature of some glaciated districts, and are explained by 
the greater amount of ice-erosion in the main valley as compared with its tributaries. If 
the pre-Glacial stream of Coir' an Lochain had been larger, and its gradient more 
moderate, something more closely comparable with the typical hanging valley might 
have resulted ; but this and other examples which might be cited in the Cuillins are 
better described as ' hanging ' cirques, or, as we have already called them, high-level 
niches. Our small area does not comprise many tributaries of more than very moderate 
dimensions. The best example is Tairneilear, which debouches some 250 or 300 feet 
above the floor of Coir' a' Mhadaidh or Coire na Creiche, and may be taken as a fairly 
typical hanging valley. 

Professor Davis lays stress especially upon the deepening of the main valley. 
Either deepening or widening may conceivably bring about the result, though the 
former at a greater cost of total erosion. In the middle and lower courses of valleys 
like those of the Cuillins we have already seen reason to attach special importance to 
glacial erosion in the lateral direction, but we shall see that in some circumstances there 
has also been a considerable amount of erosion in the vertical sense. 



(vii.) Cirques: Character of Ridges. 

We come next to what is perhaps the most striking characteristic of the surface- 
relief of the Cuillins, viz., the evidence of excessive erosion in the upper parts of all the 
valleys. Quite apart from what has been described in other countries, we should be 
led by general considerations to connect this peculiarity with glacial erosion. As we 

* W. M. Davis, "Glacial Erosion in the Valley of the Ticino," Appalachian vol. ix. jrp. 136-156, pi. xv., xvi., 
1900 ; "Glacial Erosion in Fiance, Switzerland, and Norway," Proc. Bost. Soc. Nat. Hist., vol. xxix. pp. 273 322, pi. 
1-3, 1900. 



ICE-EROSION IN" THE CUILLIN HILLS, 8KYE. 



235 



N.hjW. 



have already remarked, the efficiency of erosive action at the lower surface of ice well 
supplied with rock-debris may be expected to increase, cseteris paribus, with the pres- 
sure, and therefore with the thickness of the superincumbent mass. A glacier, unlike 
a river, comes into being full-grown ; and the ice-cap which covered the Skye mountains 
during the great glaciation was, as we have urged, thickest towards the centre. 

As we pass up any of the valleys of the Cuillins, we find that the U-shape becomes 
more pronounced and the concave sweep of the transverse section more regular (fig. 5). 
Further, the valley does not contract 
towards its head, but shows a decided 
expansion (figs. 3 and 4). These points 
may be made out to some extent on 
the contoured Ordnance Map; and even 
in our map it is noticeable that the 
concave portions of the 2000-feet line 
have the sweeping curve of bays. In 
some places these contrast with sharper 
indentations of the 1000-feet line, 
but this point would come out more clearly if the line corresponding with 1500 feet 
were drawn. 

The expansion, becoming more marked towards the head of the valley, culminates 
in a cirque or typical corrie in the strict sense.* In vertical section the simple cirque 
presents a flowing concave curve up to the actual crest-lines of the bounding ridges, 
and the form is the same in longitudinal as in transverse section (fig. 6). More 
accurately, these terms cease to have any meaning ; for there is no longer any 




Fig. 5. — Two transverse sections of Coir' a' Ghreadaidh : 
scale, about 2J inches to a mile. 




S.S.w. 



N.N.E. 



jfie. g, — Longitudinal profile of the floor of Coir' a' Ghrunnda ; scale, about 2J inches to a mile. Also another section across 
the cirque which forms the head of the valley. 

L is the tarn at the bottom of the cirque ; M the crescentic moraine opposite the mouth of the valley, described 
below. 

' Thalweg,' or rather the whole surface of the cirque may be regarded as the Thalweg. 
If part of the water which courses down the slopes collects into gullies or other 
channels, these are to be regarded rather as incidents not essential to the typical cirque. 
This presents the same sweeping concave form in horizontal as in vertical section, and 
may be pictured simply as the half, or rather more than the half, of a hemispherical bowl. 

* Gaelic coire, a cauldron : the term is, however, loosely applied in common usage to the whole valley. 



236 MR ALFRED HARKER ON 

A common incident of the cirque is a small rock-basin on its floor, occupied of 
course by a tarn. The altitudes of the principal examples in the Cuillins are as 
follows : — 

Coir a' Bhasteir, ..... 2250 feet. 

Coir' a' Ghrunnda, . . . 2220 „ 

Coir' an Lochain, . . . . . 1815 ,, 

Coire Labain, ..... 1805 ,, 

These high-level tarn-basins, a consequence of that excessive erosion in the head 
portion of the valleys to which we have adverted, are of different significance from the 
elongated lake-basins to be noticed below. They are of small dimensions, and approxi- 
mate to the circular form. Though we have not sounded any of them, it is clear that 
they are of comparatively small depth. Tn a cirque approaching most nearly to the 
ideal form the tarn occupies the exact centre ; but if there is any tendency to 
elongation in the direction of the valley, the tarn is found a little further down 
(compare figs. 3 and 4). 

The concave upward sweep of the cirque continues, as has been said, to the actual 
crest-line. Hence arises the characteristic cuspate form in cross-section of the main 
lost) ridge of the Cuillins, and the adjoining 

portions of the chief branch ridges ; a 
form illustrated by a rather extreme 
example in fig. 7. In every place the 
ridges are very narrow and the slopes 
very steep. Here we must make a 
remark of considerable importance in this 
connection. The erosion in the higher 
corries of which we have been speaking 
NNE SSwImnw S c; F was °^ course dependent upon an adequate 

„ Z ~Z~7. . , „ , . ~ ~ r n ■ > . x» T • supply of abrading material at the under 

Fig. 7. — Section across the Basteir ridge from Coir a Bhasteir i. I J o 

on the north to Lota Corrie on the south ; scale, about 4J Surface of the ice. On the principal 
inches to a mile. . , , . . . . . 

ridges, which we have shown acted as 
ice-sheds, ice-erosion necessarily failed for want of a tool to work with. Hence, as 
the excavation of the cirques proceeded, the dividing ridges were left standing out in 
more and more salient relief. Thus arises that knife-edge form of the ridges which 
makes them the delight of climbers. Hence, too, the peculiarly unbroken character of 
the main ridge as a whole. From Sgiirr nan Gillean to Gars-bheinn it extends seven 
miles, and nowhere presents anything that can be called a pass in the usual sense. 
Although only the higher peaks rise above 3000 feet, the ridge never falls below 2500. 
A stranger ascending one of the valleys, where he looks for a pass at the head, is 
confronted by a precipitous rock-face, viz., the back wall of the cirque. 

Just as each portion of the main watershed — once the ice-shed — is merely the 



21 SO 



ICE-EROSION m THE CUILLIN HILLS, SKYE. 237 

cuspate septum left by the excavation of two opposed cirques, so each culminating 
peak is in general the triangular pyramid left in the midst of three such cirques. 
The form is not strictly pyramidal, for the cirques are concave in horizontal as well 
its in vertical section, so that the ground plan of each peak comes to have the outline 
of a tricuspate curve which is highly characteristic. This is well shown by the 
3000 feet contour-line on the map given below. Bidein Druim nan Ramh and 
Sgiirr a' Ghreadaidh, standing each in the midst of four corries, are four-cusped 
instead of three -cusped. The former of these mountains and the subsidiary spurs 
of the latter do not reach 3000 feet, but their shapes are partly indicated on the map 
by the 2000-feet line. 

(viii.) Longitudinal Profile of Valleys : Lake-Basins. 

We have next to examine the form of the valleys in longitudinal section along 
tlie actual main drainage- line or 'Thalweg'; and we observe at the outset that 
this line is by no means always concave upward, nor does its declivity show anything 
like a steady diminution from the head to the outlet of the valley. If we may take 
the Cuillin district as a type, it appears that ice-erosion does not, like water-erosion, 
work constantly towards the establishment of an even gradient along a valley in which 
it operates. It tends, not to reduce, but to exaggerate within certain limits the more 
marked inequalities of the longitudinal profile ; and in some circumstances it may 
set up a negative gradient in a certain portion of the valley. 

The bed of a river which has attained a mature state maintains a steady 
gradient so long as the volume of water is unchanged, and the gradient diminishes 
down-stream in a manner proportioned inversely to the increasing volume. This law 
is a consequence of the relations which necessarily subsist between declivity, velocity, 
volume, and load. Perhaps the clearest presentation of the argument is that in 
Gilbert's Geology of the Henry Mountains ; and a glance over his treatment of the 
subject is sufficient to show that these fundamental principles in the case of water 
have no counterpart in the case of ice. On the other hand, it appears that in 
ice-erosion certain other principles will come into operation which are peculiar to this 
agency. Thus we may expect that, other conditions being the same, erosion will be 
most efficient where the pressure below the ice is greatest, i.e., where the thickness is 
greatest. If the longitudinal profile of a valley be of irregular form, while the upper 
surface of the ice declines steadily, the thickness will be greater over parts which have 
re-entrant or concave forms than over adjacent parts which have salient or convex 
forms ; and, on the principle laid down, differential erosion will operate so as to 
exaggerate the inequalities. The original inequalities postulated must have a certain 
magnitude. On the other hand, the condition that the upper surface of the ice declines 
steadily implies that they must not be too great in proportion to the thickness of the 
ice. Within these limits it appears that the steady gradient, which for water-erosion 

VOL. XL. PART II. (NO. 12). 2 N 



*238 Ml! ALFRED HAEKEB ON 

is the stable form, is for ice-erosion unstable, since any departure from it leads to a 
further departure. There must, of course, be a limit to the action described, viz., when 
the lower layers of the ice begin to be ponded in the lee of a strong feature, and the 
upper layers slide over them. 

These remarks receive striking illustration in the Cuillin Hills. Excluding the 
three main interior valleys, which in no part reach more than a very moderate altitude, 
all the glens show a very remarkable configuration. The longitudinal profile consists 
of two or three stretches of moderate slope divided by relatively steep drops, over 
which the water cascades. Where two such drops occur, as in all the longer valleys, the 
upper one is both higher and steeper than the lower. The heads of some of the glens, 
such as Coire na Banachdich, Coir' a Ghrunnda, and Coire nan Laogh, are almost 
inaccessible from below ; and to an observer coming into the district for the first time 
this stepped or storeyed form of the valleys is one of its most conspicuous peculiarities. 
The more or less precipitous drops, which constitute the steps and separate the 
successive storeys, are in no instance connected with anything in the geological 
structure of the ground, and there is no correspondence as regards levels between 
even adjacent valleys. In typical examples the descent is usually 200 to 400 feet, 
with an average gradient which varies in different cases from 30 to about 70 vertical 
in 100 horizontal. The best example of a valley divided into three parts by two steep 
drops is the one made up of Lota Corrie and the upper part of Harta Corrie.* Coir' a' 
Ghrunnda (fig. 6) illustrates a different case, the upper part of the Corrie being cut off 
by two sharp drops close together, giving a total fall of about 850 feet in a horizontal 
distance of 2100 feet. 

Apart from superficial accumulations which may complicate the conditions — a case 
with which we are not concerned in the Cuillins — a negative or reversed gradient in 
the ' Thalweg ' implies, of course, a rock-basin, and is, as Ramsay long ago pointed out, 
a result which cannot be arrived at by aqueous erosion. There is, in the opinion of 
the present writer, some danger of attaching too much weight to rock-basins as 
phenomena indicative of ice-action, with the result of diverting attention from other 
phenomena equally characteristic and often of a larger order. That the floor of a 
valley is lower at a certain place than at another place farther down-stream is of 
interest because it is an absolute criterion, not one of degree ; but to dwell unduly 
upon this is to treat the rock-basin as an isolated phenomenon instead of what it is, 
viz., an integral part of the valley. It is an incident, depending not merely on glacial 
erosion, but on glacial erosion operating under certain local conditions. The requisite 
conditions may be realised in more than one way ; and in a classification of the 
characteristic forms of ice-erosion according to their origin and essential significance 
different rock-basins would fall under different heads. 

Of the three main interior valleys of the Cuillins, two, viz., those of Coruisk and 
Camasunary (Strath na Creitheach), contain elongated rock-basins. The determining 

* See section, Oeol. May. 1 899, p. 1 97. fig. 2. 



ICE-EROSION IN THE CUILLLN HILLS, SKYE. 



239 



condition in both cases was the same, a marked constriction of the valley towards its 
lower end, which must have occasioned a certain heaping up of the ice in that part. 
In Coruisk the constriction was caused by the Sgurr Dubh ridge running out eastward 
from the main range ; in the Camasunary valley the same effect was produced by the 
convergence southward of the flanking ridges, Blath-bheinn on the east and Druim an 
Eidhne, Sgiirr an Eidhne, and Sgurr na Stri on the west. The third main valley, 
that of Sligachan, opens out towards its lower end, and there is accordingly no 
rock-basin. 

With the kind co-operation of Mr T. A. Falcon, a series of about 150 soundings 
have been taken in Loch Coruisk, and the results are embodied in the rough contoured 
map given in fig. 8. Owing to practical difficulties,* the soundings are rather deficient 




sa I CONTOUR LINES 

T S DEPTH III FEET 

100 J 



-©»■ &L«CI»L STRI/E 

SHINGLE DELTAS. 



Fig. 8. — Bathymetric map of Loch Coruisk, plotted from 150 soundings taken by T. A. Falcon and A. Hakker. The 
actual soundings are given only in places where the contour-lines alone do not suffice to render the form of the bottom. 
The water-surface is 26 feet above sea-level. 



in places, and unfortunately so in the deeper part of the loch ; but the general form 
of the bottom is rendered with sufficient accuracy for our purpose. It will be seen 
that there are in reality two basins, the maximum depth being nearly 90 feet in the 
upper one and 125 feet in the lower, which latter goes nearly 100 feet below the 
sea-level (O.D.). These two basins are separated by a shallower area, never exceeding 
40 feet in depth and rising in several places into small islets. The bottom is in 
general of bare rock. The shallow head of the loch is partly filled by a flat shingle 
delta, and the bottom is also shingly in places along the south-western shore ; but these 
accumulations are nowhere in such force as to prevent the soundings giving very closely 
the true shape of the rock-basin. This seems to differ in no respect, as regards detailed 
sculpture, from the shape of the valley bottom where it does not happen to be covered 

* The principal difficulty was in finding sufficiently calm weather. In a wind it was found impossible to keep 
the boat in place while a sounding was made and the position determined. 



•240 MR ALFRED HARKER ON 

by water; but the soundings taken are not numerous enough to bring this out in the 
lower and deeper of the two basins. 

In the Camasunary valley there are two lakes, the upper and smaller Loch an 
Athain and the lower and larger Loch na Oreitheach. The latter is visibly rock-bound 
except at its head, where a gravel flat intervenes, which extends up to Loch an Athain 
and some three-quarters of a mile further. The form of the rock-surface is thus obscured, 
but it seems almost certain that the two lakes lie in separate basins. The proprietor, 
^\lr R. L. Thomson, had some soundings taken, and has kindly communicated the result. 
The greatest depth found in Loch na Creitheach was 91 feet, at a point about one- 
third up the loch from the S. end and a quarter across from the W. side. As the 
water-surface is 85 feet above the Ordnance Datum, the loch descends about 6 feet 
below this. Loch an Athain (111 feet above O.D.) has only about half the depth of 
its larger neighbour. 

(ix.) Asymmetric Element in the Surf ace- Relief . 

The last peculiarity to be mentioned in the topography of the Cuillins is one 
which is very evident when once pointed out. It is observable, not in the central, 
but in the peripheral parts of the mountain-area ; and takes the form of a decided 
asymmetry, as between the northerly and southerly aspects, in the transverse section 
of any element of the relief (ridge or valley) which has something of an E. to W. 
trend. The northward-facing slopes are invariably steeper than those facing in the 
opposite direction. There is nothing in the geological structure of the ground to 
account for this, and it is certainly too prevalent a phenomenon to be dismissed as 
fortuitous. The only reason which suggests itself for this dependence of the character 
of a mountain-slope upon its aspect, is one which connects it with the direction of 
incidence of solar radiation. 

The asymmetric character is almost lost in the central parts of the area, but 
declares itself more and more as we approach the margin. This is shown, e.g., in the 
two sections across Coir' a' Ghreadaidh given above (fig. 5) ; but the point perhaps 
comes out more clearly if we consider, not the valleys, but the ridges, i.e., those of the 
exterior branch ridges which have (as is mostly the case) something of an easterly or 
westerly direction. Any one of these in its higher or proximal portion, where it 
forms the boundary between two cirques, shows the same general shape as the main 
ridge. Farther away it changes its character. It may or may not abate something of 
its steepness, and in some cases it becomes round-backed, though still with relatively 
steep flanks; but in every case the contrast between the two faces declares itself in 
the distal portion of the ridge (fig. 9). The westerly spurs of the Cuillins are Sgiirr 
Thiiihn. Sgiirr' nan Gobhar with its offshoot An Diallaid, Sgiirr Dearg (west ridge), 
and Sgiirr Sgmnain, to which we. may add the west ridge of Gars-bheinn. On the 
opposite side of the gabbro mountains we have Belig, Sgiirr nan Each, and the 



ICE-EROSION IN THE CTJILLIN HILLS, SKYE. 



241 



easterly spurs of Clach Glas and Blath-bheirm. Each of these ten branches has a 
precipitous face towards the north and a less steep slope towards the south, though 
the chances against such a coincidence as an accident are more than a thousand to one. 
It may be noticed, too, that the only 
parts of the main ridge of the Cuillins 
which have the E. to W. direction, viz., 
the Basteir and Sgiirr a' Mhadaidh, are 
also steeper on the north side than on 
the south (fig. 7). 

The distribution of the cirques or 
true corries in the Cuillins and the 
adjacent Red Hills also suggests a con- 
nection with the direction of sunshine. 
Helland* long ago pointed out that 
in Norway most of the cirques face 
northward, or towards some point of 
north ; and something of the same kind 
is to be noticed in the Skye mountains, as appears from the following table giving the 
aspects of 52 cirques : — 




N.W 



S.E. 



Fig. 9. —Transverse section of lower part of the Sgurr Sgumain ridge, 
to show its asymmetric form. The dotted line gives for com- 
parison the symmetrical cuspate cross-section of the higher 
part of the ridge. Scale, about 3^ inches to a mile. 



W.N.W. 


4 


N.W 


2 


N.N.W. 


3 


N. 


8 ) 


N.N.E. 


4 


N.E. 


8 I 


E.N.E. 


2 


E. 


6 




37 



20 



E.S.E. 


1 


S.E. 


3 


S.S.E. 


1 


S. 


1) 


S.S.W. 


4 


s.w. 


2 J 


W.8.W. 


1 


W. 


4 




15 



The inequality here, though decided, is not overwhelming, and except in con- 
nection with the foregoing remarks would not call for notice. It should be remembered, 
however, that we have included here the interior of the district, where the influence 
of aspect is much less evident than towards the exterior. If we separate the interior 

from the exterior corries, we find — 

N., etc. S., etc. 



Interior 
Exterior 



18 
19 



12 
3 



Here the prevalence of the northerly aspect in the second group of cirques is very 
marked. The basaltic plateaux beyond the mountain district owe their form almost 
everywhere to their geological structure, but even here there are some significant 
exceptions. An Cruachan, for instance, a hill to the west of Glen Brittle, presents a 

* Quart. Jonrv. Geol. Soc, vol. xxxiii. pp. 162, 163, 1877. 



'242 MR ALFRED HARKER ON 

bold range of cliff, partly enclosing a come, to the north and a gentler slope to the 
south, though the dip, which is northerly, would lead us to anticipate the reverse. 

If, as I believe, the asymmetric character of the ridges and valleys in the outer 
parts of the mountain area is really significant, and depends upon the different aspects 
of the slopes relatively to the sun, it seems clear that this influence was exerted, not 
at the stage of maximum glaciation, but when the ice-cap had shrunk so as to occupy 
the valleys alone, and during the later glaciation, which was effected by glaciers only. 
In the preceding sections I have not attempted to apportion the work of erosion 
between the ice-cap and the glaciers. I have in more than one place postulated a 
great thickness of ice over the centre of the area, and it is to be inferred that some 
of the most characteristic features of the district, especially in its interior part, were 
developed under such conditions ; but we may still allow no inconsiderable role as 
agents of erosion to the glaciers, more particularly in the middle and lower courses of 
the mountain-glens. It is possible that a more thorough analysis might enable us to 
discriminate, by means of the resulting surface-relief, between the sculpture of a valley 
by a limb of an ice-cap on the one hand and by a glacier on the other, both being- 
assumed to move down the valley. At present we are only concerned in distinguishing 
these two jointly from a foreign ice-sheet forced across the face of the country with 
scant regard to the pre-existing form of the ground. From the foregoing brief 
examination of the peculiar type of surface-configuration presented by the Cuillins, 
it has been made sufficiently clear that most of the positive characteristics, i.e., those 
involving the development as distinguished from the obliteration of features of relief, 
depend upon the fact that the flow of the ice followed, in general and upon a broad 
scale, the natural direction of drainage. That in other circumstances the results miarht 
be very different is suggested by several of the phenomena described above. A good 
illustration is afforded by the small pre-Glacial glen of Allt a' Coir' an Lochain, a type 
of numerous others in the district. Here, as we have seen, the movement of the ice 
in the upper part of the valley was down-stream, but in the lower part directly at 
right angles to it. The result has been that the head of the glen is enlarged and the 
lower portion completely obliterated. 



III. The Glacial Accumulations and their Testimony to Ice- and 

Frost-Erosion. 

(x.) Drift Deposits. 

We turn now from erosion to the complementary process of deposition ; but, in 
accordance with the general design of this contribution, the glacial accumulations will 
be considered chiefly as throwing light upon the subject of ice-erosion. Drift deposits 
are found, though not as an unbroken sheet, over the whole of the tract that lies 
beyond the mountains. The continuous deposits — i.e., excluding scattered erratics — 



ICE-EROSION IN THE CUILLIN HILLS, SKYE. 243 

ascend usually to heights of 800 to 1000 feet, or sometimes as much as 1300 feet, on 
the higher moorland hills ; only in places near the coast does the drift-line sink much 
lower, and even locally to sea-level. In the mountain- valleys the drift, always with 
diminished thickness, runs up in tongues to altitudes of 1000 to 1500 feet, and 
exceptionally 1750 feet. 

We are here referring to the tract within which the glaciation was strictly local. 
The limits of this tract are partly laid down in the small sketch-map given above 
(fig. 1). Within it, the boulders are wholly derived from the tract itself, thus present- 
ing a marked contrast to the area outside the line drawn. In the south-eastern part 
of Skye, Mr Clough has found foreign boulders even up to the highest summit (Sgurr 
na Coinnich, 2400 feet). The same observer notes along Loch Eishort a certain 
intermingling of boulders from different sources, which may be taken to indicate some 
oscillation of the line where the native and foreign ice marched together. Such 
oscillations, depending on the balance of varying pressures, are to be expected. On the 
north-eastern side of our area the domain of the native ice is delimited with sufficient 
closeness. Especially marked is the contrast between Scalpay and the neighbouring 
part of Skye. On the smaller island, which was overflowed by the great ice-sheet 
from the mainland, boulders of Scottish extraction occur at all altitudes, and in the 
boulder-clay no less than on the surface, while further points of difference are apparent 
in the nature and distribution of the drift and in the form of the ground. Raasay 
evidently falls under the same head. Our detailed survey of Skye has not progressed 
far enough northward to trace the boundary-line in that direction, but the breaking 
in of the Scottish ice over the northern part of the island seems to be sufficiently 
established. 

A closer examination of the materials of the local drift affords much information 
relative to the movement of the Skye ice, and also leads to observations which have a 
very direct bearing upon the amount and the mechanics of glacial erosion. Since in 
the area chiefly involved the number of local rocks which can be readily identified is 
not great, it becomes necessary to take note of the relative proportions in which 
different rocks enter into the composition of the accumulations. The writer has found 
that for this purpose general impressions are not to be trusted, and he has followed 
as far as possible the statistical method. As an illustration of the use of this, as well 
as for some of the results obtained, we will follow the course of what we have already 
referred to as the mid-stream line of the Glen Sligachan ice (see map below). To lay 
down this line, about a hundred convenient stations were selected, and at each station 
from 200 to 500 boulders were taken without selection from the drift and the per- 
centages of different rocks estimated. 

Looking down Glen Sligachan from the watershed at Loch Dubh, the observer 
has the Red Hills on his right and the Cuillins on his left. The former are essentially 
of granite, the latter of gabbro ; the line of junction of the two rocks running for some 
distance along the bottom of the valley. Accordingly granite boulders preponderate 



•244 Mil ALFRED KAIIKEK ON 

in the drift on the right side of the valley and gabbro boulders on the left. A line 
drawn down the valley through places where the two rocks are equally represented 
is what we have styled the mid- stream line of that branch of the ice which took this 
direction. This line can be drawn with considerable precision, since the relative pro- 
portions of the two rocks vary rather rapidly as we cross the floor of the valley. Thus, 
at or near Loch Dubh, the percentages of granite and gabbro are 76 and 15 at 70 
yards to the right (i.e., E.) of the line, 86 and 4 at 250 yards, and 98 and 2 at 450 
yards; while to the left (or W.) of the line there is an equally rapid change in the 
opposite sense. The 100 per cent, is made up by boulders of basalt (including dolerite) 
and, at this place, volcanic agglomerate. We have not always found it possible to 
discriminate with certainty between the basalt lavas and the basalt and dolerite dykes 
and sheets, but at this place the latter must supply the chief contribution. 

Proceeding down the glen, we find that the line can be traced throughout with 
sufficient accuracy. Near the outfall of Allt Coire Riabhach, for instance, the per- 
centages of granite and gabbro are 55 and 36 to the right and 7 and 67 to the left, 
the two spots being only 40 yards apart. Here, as in other places where it is most 
sharply defined, the line coincides exactly with the junction of granite and gabbro in 
place. Indeed, there are many circumstances which seem to indicate that the 
immediately subjacent rocks have contributed an important part of the boulders. 
This becomes very clear when, about 1^ mile above Sligachan, we come on to the 
basaltic lavas. At once the proportion of those miscellaneous basaltic boulders which 
we have grouped together as the third element begins to increase rapidly, and 700 or 
800 yards lower down they already make up 65 to 80 per cent, of the whole, instead 
of 10 per cent, or less. It is clear, too, that the bulk of these basalt boulders are of 
the lava type, and they must indisputably have been torn from the floor of this broad 
open strath. 

From Sligachan bridge, being now clear of the mountains, the line curves away 
in accordance with the general westward deflection already considered, sweeping round 
b}^ Loch M5r na Caiplaich into the Drynoch valley, where for some distance it runs 
very near the D un vegan highroad. The percentage of basaltic boulders has now risen 
to 90 or 95 or even 98 or 99, mostly amygdaloidal lavas, so that it becomes necessary 
to examine a larger number of boulders in order to determine the proportions of granite 
and gabbro with sufficient exactness.* Before reaching Drynoch our line takes a curve 
to the south-west, rising to about 500 feet and coming down to the valley of the 
Vikisgill Burn. Crossing this, it passes southward up a tributary valley, Allt na 
Qreadha, over a third watershed (about 550 feet) into the valley of Allt nam Fitheach, 
and so south-west to the sea at Loch Eynort, having traversed a semicircle from 
Sligachan. 

To the left of the line as thus traced, gabbro boulders are in force, while those of 
granite become rare ; though a few of the latter are still found as much as 1\ miles 

* Farther west the basalt has often been discarded and only the granite and gabbro boulders counted. 



ICE-EROSION IN THE CUILLIN HILLS, SKYE. 245 

away, at the upper bridge over the Brittle Kiver, which point they have reached by 
way of Bealach a' Mhaim. To the right of the line the reverse is observed. Two 
miles away, about the head of the Eynort River, the granite boulders are about ten 
times as numerous as those of gabbro, and beyond this the latter are rare. Granite is 
plentiful between Loch Eynort and Loch Harport, boulders up to 2 feet in diameter 
occurring, for instance, on the top of Preshal Beg (1160 feet) near Talisker. It is, of 
course, not to be assumed that all the granite necessarily comes from Glen Sligachan 
and the hills overlooking it ; for that part of the ice from the central and eastern Red 
Hills which found an outlet to the north must have been forced westward by the 
Scottish ice-sheet before the latter itself effected a landing on the northern part of 
Skye. That the Sligachan ice spread over a very wide tract is nevertheless proved by 
boulders of certain easily recognised rocks ; e.g. , a pitchstone from Glamaig, a grano- 
phyre crowded with ovoid patches of a basic rock from Glamaig and Srbn a' Bhealain, 
and a granite enclosing gabbro debris from Marsco. 

There is no need here to trace out in the above fashion all the other branches of 
the ice from the Cuillins. Their course cannot usually be followed with the same 
precision as above over the low ground ; unless, indeed, boulders of some local and 
distinctive rock be available for the purpose, such as the rhyolite, etc., of Fionn-choire 
and the picrite of Coir' a' Ghrunnda. Wherever the test can be applied, we find a very 
close correspondence between the transport of boulders and the direction of striae ; 
which would not always be the case if the boulders had been to any important extent 
carried on the ice or in its upper part. The manner in which the basaltic boulders 
always become increasingly abundant as soon as we pass from the gabbro to basalt in 
place is especially striking. Since it is certain that no basalt stood out above the ice, 
this proves that, at least in the belt of country bordering the mountains, a very con- 
siderable amount of erosion of the basaltic ground went on beneath the ice. Further, 
this erosion, in so far as we have direct evidence of it, was effected not merely by 
abrasion but by fracture of the surface rocks. 

This last point calls for further remark, for the importance of ice-action in tearing 
away pieces of the subjacent rocks is one of the most salient facts of glacial erosion in 
our area. It is emphasized by the large proportion which boulders bear to matrix in 
all the glacial accumulations in the vicinity of the mountains. To such action also we 
must ascribe the rough craggy surface (certainly not the pre-Glacial surface) seen often 
on the lee side of a roche moutonnee just outside the mountains. In the interior of 
the mountain-area, as already remarked, this is not usually seen, and the inference 
suggested is that fracture of rocks is not so readily effected under a great pressure of 
ice. If there be truth in this, it is still only one of the factors which determine 
whether a rock shall yield by grinding down or by tearing away. The nature of the 
rock is doubtless another factor, and an important one, especially as regards the 
presence or absence of joints or other lines of weakness. In this connection it is to be 
noticed that in the drift of the mountain-area proper boulders from the basic dykes and 

VOL. XL. PART II. (NO. 12). 2 



246 MR ALFRED HARKER ON 

sheets intersecting the gabbro invariably play an unduly prominent part as compared 
with the boulders of gabbro. The composition of the drift in the lower corries is, 
indeed, very remarkable. Tairneilear is a good example, since here the question is not 
complicated by patches of basaltic lavas enclosed in the gabbro. The bare surface of 
the corrie is composed of gabbro intersected by dykes and sheets of basalt and dolerite. 
These minor intrusions, though very numerous, make up but a small part of the whole : 
probably one-twentieth would be an over-estimate. When, however, towards the 
mouth of the corrie, we come upon the drift, we find that boulders of these rocks make 
up, not one-twentieth, but from one-third to one-half of the total boulders. Clearly 
some selective influence has operated. Since the average constitution of the drift must 
be the same as that of the rocks in place, we conclude that the jointed and brittle 
rocks of the minor intrusions have mostly broken away and formed boulders, while the 
more massive gabbro has in much greater measure been ground down and gone into the 
matrix. 

Hitherto we have made no classification of the drift accumulations. The more or 
less continuous deposits with which we have been dealing, seem to belong wholly to 
the time when the flow of the Skye ice outside the mountain-area was diverted in the 
manner already described by the pressure of the Scottish ice-sheet. Among them we 
may, however, distinguish two types : one corresponding with the phase of maximum 
glaciation, when central Skye was covered by a continuous ice-cap ; the other connected 
with the waning phase of this principal glaciation, when only fragmentary relics of the 
ice-cap remained. The most widely spread type of drift in our area has the ordinary 
characters of a ground-moraine. In the valleys and on the lower slopes of the basalt 
country, where it is best displayed, it imparts to the landscape the familiar gently 
undulating appearance with smooth flowing outlines. Here it consists of a reddish 
sandy clay enclosing numerous small boulders and some large ones, often planed and 
scratched. Elsewhere its composition varies to some extent, the local element being 
always important. The second type is what we have called in mapping the country the 
' hummocky ' drift, and it seems to answer to the ' kettle-moraine ' of some American 
geologists. The ground is closely studded with circular mounds, like tumuli, usually 
from 10 or 15 feet to 50 or 60 feet in height, only rarely showing any linear or other 
arrangement. The finer material, which may be regarded as a matrix, is commonly 
reduced to a minimum, the bulk of the accumulation consisting of boulders, mostly 
subangular but rarely scratched. It is often noticeable that the larger boulders occur 
towards the summit of the mound. The hollows of the irregular surface frequently 
hold tarns, from 300 or 400 yards long down to mere pools, those in the neighbourhood 
of Sligachan being good examples. Loch an Fhir-bhallaich, near Glen Brittle, illus- 
trates another kind of tarn, occurring above and outside the margin of an area of 
kettle-moraine, but held in by it. 

The hummocky drift has a much more restricted distribution than the smooth, and 
this distribution is a significant one. The patches of hummocky drift lie constantly 



ICE-EROSION IN THE CUILLIN HILLS, SKYE. 247 

within the area occupied by the smooth ; they do not extend so far from the mountains, 
and on the other hand they do not enter the mountain-tract itself except along the 
floors of the wide and level interior valleys. This type of drift is indeed confined to 
open places, usually near the mountains, in parts where the slope of the surface is 
gentle, and it is found in such places especially where the flow of the ice has been 
obstructed or checked by extraneous interference. The finest development is in the 
Red Hills tract, and more particularly at such places as Luib and Strollamus, where 
considerable branches of the native ice abutted directly upon the flank of the Scottish 
ice-sheet. In the part of the island which we have chiefly considered, the largest area 
of hummocky drift is that near Sligachan, extending from Harta Corrie to near 
Garadubh, on the Portree road, a distance of ten miles. Arms of this extend up the 
valley of Allt Dearg Mbr and over into the Drynoch valley for distances of 1 mile and 
1^ miles respectively, and there is a detached area in Coire Keidh na Loch. Patches 
occur again in Strath na Creitheach and the open part of Coire Riabhach, between 
Druim nan Ramh and Druim an Eidhne, and others on the west side of the Cuillins, 
viz., south of Coir' a' Ghrunnda and between Allt Coire La bain and Allt Coire na 
Banachdich. The most remote isolated occurrence observed is a small patch at the 
head of the Talisker valley. 

The phenomena in the Skye district, viewed generally, seem to find their simplest 
explanation on the supposition that the waxing and waning of glacial conditions have 
been controlled less by secular changes in the mean temperature than by variations in. 
the amount of precipitation over the area. This question could not be profitably 
discussed as a local one. But whatever the causes which terminated the maximum 
glaciation of central Skye, it cannot be doubted that the ice -cap shrank away from the 
mountains as well as from its margin. As the steep summit-ridges emerged, there 
was added a new element of ice-transport by the accumulation of material upon the 
upper surface of the ice ; an element increasing in relative importance as the erosive 
effect at the lower surface became feebler. We interpret the hummocky drift as 
the materia] — superglacial, englacial, and infraglacial — finally deposited by stranded 
portions of the confluent glaciers, cut off from their supply behind and melting as they 
stood. All the features of its composition, no less than its distribution, seem to accord 
best with this view. The absence of all ordinary morainic accumulations referable to 
this epoch suggests that the disappearance of the ice was a somewhat rapid event. It 
is clear, from the dispersal of boulders, that no change in the direction of the ice- 
drainage took place from the maximum glaciation to the close of this phase, such lines 
as that already noticed marking the mid-stream of the Sligachan branch being traceable 
uninterruptedly through the smooth and the hummocky drift alike. 



24 8 MR ALFRED HARKER ON 



(xi.) Later Glaciers and Frost-Erosion. 

In numerous parts of Scotland geologists have recognised two more or less distinct 
glaciations, the first a general one and the second a local. In the central part of Skye 
also there is clear evidence of two glaciations. though — since foreign ice never obtained 
a footing here — they cannot be distinguished in those terms. That the second 
glaciation here corresponds with the local glaciation in adjacent parts of Scotland, and 
was in a general sense contemporaneous with it, is evident from the map given below, 
on which the flow of the ice during this later stage is indicated by a second set of 
arrows. These have been inserted only in places where the evidence was quite clear ; 
but they suffice to show that the movement was very different on many parts of the 
lower ground from that during the principal glaciation, and that the difference was due 
to the withdrawal of the Scottish ice-sheet. Instead of the general diversion westward, 
upon which we commented before, there is now a simple radiate outflow from the 
mountains to the sea. This reversion to what we may consider the natural direction 
of ice-drainage for the district, consequent upon the removal of the constraint from 
without, involved, at many places outside the mountain area, considerable departures 
from the former directions of flow. Thus, to the north-west of the Cuillins, the new 
line of movement, directed towards Loch Bracadale, was at right angles to the old. 
In the valley of Allt Dearg M5r the direction of flow was directly reversed. In the 
earlier glaciation the ice had moved up the valley, bringing boulders from Glen 
Sligachan ; in the later glaciation it moved in the natural direction, carrying down the 
rhyolitic and other rocks of Fionn-choire and Fhinn-choire, which are found in 
abundance along the burn and to heights of 60 or 70 feet above it. The large extent 
of country overrun by the later glaciers and the way in which, in certain cases, they 
overflowed some of the lower watersheds, prove that they were of very' considerable 
magnitude, but it is clear that they were greatly inferior to the ice-sheet of the earlier 
glaciation. 

The erosive action exerted by these glaciers was mainly confined to the valleys 
of the mountain area, and was almost negligible at a distance from the mountains. 
Here it has often failed to obliterate the scorings made by the earlier glaciation, and 
has usually caused but little disturbance in the older drift accumulations over which 
it passed. Even quite near to the mountains, patches of hummocky drift have retained 
most of their characteristic appearance in places where they have certainly been over- 
ridden by the later glaciers. In the lower parts of the mountain valleys themselves, 
however, the earlier drift accumulations seem to have suffered erosion in many places. 
In certain cases, too, there are drift-ridges between the mouths of adjacent valleys, 
which seem to have been originally of the nature of drumlins, but to have been 
scarped and moulded by the later glaciers. 

The accumulations referable to this later glaciation are represented on the lower 



ICE-EROSION IN THE CUILLIN HILLS, SKYE. 249 

ground mainly by a vast number of erratics scattered over the tracks of the glaciers 
and lying thickly along certain lines and in certain places. In attempting to map 
these out accurately, considerable difficulty might be experienced in some parts in 
separating the later from the earlier deposits without suspicion of possible error. 
Where, however, characteristic rocks are available for tracing out the lines of move- 
ment no doubt can exist. For instance, as we emerge from Glen Sligachan, we find 
that the surface erratics are of granite to the right and of gabbro to the left, with only 
a narrow belt of intermingling, and we can draw a line accordingly, as already done 
for the earlier drift. We find that, instead of curving away westward, this line runs 
straight on towards Portree, only .a little on the east side of the highroad ; showing 
that these erratics were brought down at a time when the Scottish ice-sheet had 
withdrawn, or at least had ceased to press heavily upon the coast of Skye. 

To the west of this line and of the mountains, gabbro is constantly the principal 
element in these accumulations, and remains so to all distances. There are, however, 
basaltic lavas, from the patches enclosed in the gabbro mass and from the lower slopes, 
and representatives of the doleritic and other rocks of the minor intrusions of the 
Cuillins ; besides peridotites and other locally distributed types, which are found along 
lines leading from their several places. The blocks are not planed or scored. Many 
of them are of considerable size, and some very large ones are found in the lower part 
of Coire Labain, in Coire na Creiche, near the mouth of Harta Corrie, and elsewhere. 
The largest are usually of gabbro, picrite, and other massive rocks ; the more jointed 
rocks of the dykes and sheets have broken into smaller blocks ; the laminated rhyolite, 
with a slate-like fracture, is usually represented by small fragments. 

Only in a few places do these later glacial accumulations assume anything like 
the form of typical moraines. There is, however, one remarkable exception, which is 
of sufficient interest to demand notice. It occurs opposite the mouth of Coir' a' 
Ghrunnda, and was noticed by J. D. Forbes in his paper already mentioned.* Here 
we have a perfect crescentic moraine, measuring 900 yards from horn to horn and 800 
yards from that line to the front. The material consists in great part of large blocks, 
chiefly of gabbro, but including also picrite and the other rocks of Coir' a' Ghrunnda. 
The front portion is a curved ridge 150 yards across and 50 feet in height ; but 
towards the two horns the height diminishes and the width increases, until the ridge 
is represented only by a belt of closely scattered blocks. The moraine lies partly upon 
a patch of hummocky drift, which has preserved much of its characteristic surface 
relief. 

To the later glaciation must be attributed the perched blocks which are conspicuous 
objects on the bare slopes of some of the Cuillin valleys, as noticed by Sir A. Geikie. 
Good examples are seen on the western side of Sgurr na Stri, towards Lochs Coruisk 
and Scavaig, and on the lower slopes of Sgurr a' Coir' an Lochain. In the latter place 

* On Forbes' small sketch-map Coir' a' Ghrunnda appears as "Bottomless Corry." The moraine is marked 
with the letter E on our map ; see also fig. 6. 



250 



MR ALFRED HAKKER ON 




Fig. 10. — Perched blocks on the lower slope of Sgurr a' 
Coir' an Lochain, towards Coruisk. 



there are some of peridotite, which, in virtue of the excessively rough surface presented 
by that rock, have been able to take a very remarkable posture (fig. 10). 

Although the glaciers while in the mountain-glens may have exercised a con- 
siderable erosive action upon their beds, it seems evident that the blocks of gabbro 

and other rocks which constitute most 
of the accumulations which can be con- 
fidently referred to the later glaciation 
were only transported, not detached, by 
the ice. They were broken away from 
the parent rock on slopes overlooking 
the glaciers by subaerial agenc}^, in which 
frost must have been the most import- 
ant factor. To an observer approaching 
the Cuillins by any of the principal glens, 
or still better by Loch Scavaig, one of the 
first things to strike the eye is the strong 
contrast between the smooth rounded 
form of the lower slopes and the splint- 
ered shapes of many parts of the higher 
ridges. It might be hastily inferred that 
these latter have never been submerged 
beneath ice ; but such an explanation would soon be found to break down when applied 
in detail, and we have already seen from other considerations that it is inadmissible. 
There are two reasons for the higher ridges and summits not showing the effects of 
glaciation in the same way as the corries below. Firstly the ridges, acting as ice-sheds 
at the time of the maximum glaciation, escaped erosion owing to the lack of rock- 
debris in the ice overlying them, which left it almost powerless ; and secondly, the same 
ridges, exposed above the ice-surface during the later glaciation, were then subjected to 
the splintering and shattering action of frost. 

The operation of what we may call frost-erosion was not confined merely to the 
time when the valleys were occupied by the later glaciers. The requisite conditions, 
viz., a sufficiency of moisture and an air-temperature fluctuating above and below the 
freezing-point, must have existed during a part of the interval between the disappear- 
ance of the ice-cap and the birth of the later glaciers, and certainly continued for some 
time after these glaciers had vacated at least the upper parts of the mountain glens. 
This is part of the evidence, already alluded to, which goes to show that, in determining 
the glaciation of this part of the country, variations in the amount of precipitation 
were of greater moment than variations in mean annual temperature. The proof that 
the later glaciers withdrew from at least the upper parts of the glens while a severe 
temperature still prevailed, is afforded by a class of accumulations not hitherto 
mentioned, viz., the huge taluses which are so conspicuous a feature of almost all the 



ICE-EROSION IN THE CUILLIN HILLS, SKYE. 251 

hio-her corries of the Cuillins. These have not the character of screes resulting from 
modern subaerial waste; and indeed, despite an increased elevation amounting to 100 
feet, the actual waste under existing conditions is exceedingly small.* Certainly it 
is inadequate to account for more than a very small fraction of the material which 
chokes the heads of many of the glens. 

While the great taluses, composed mainly of blocks of gabbro and the associated 
rocks, on the slopes and much of the debris on the floors of the corries have clearly 
reached their present situations by falling, rolling, and sliding, probably assisted in 
part by snow-slopes, it is often impossible to divide these accumulations from the 
similar material farther down-stream, which has doubtless been ice-borne, probably on 
the tail of a dwindling glacier. A good instance of this difficulty is seen in An G-arbh- 
choire. the glen to the south of the Sgurr Dubh ridge. The whole length of the 
valley, about a mile, is rendered almost impassable by the blocks, great and small, here 
chiefly of peridotites, by which it is covered. These cannot be separated distinctly 
from the more scattered blocks over the little plateau between the mouth of the glen 
and Allt a' Chaoich. In the lower part of the valley the peridotite blocks must have 
travelled down, for the slopes on both sides are of gabbro ; but the higher part of the 
accumulation is merely a great talus streaming down from the steep main ridge. 
Something of the same kind is seen in Coireachan Ruadha, where the taluses of gabbro 
and peridotite blocks are on a large scale. Among the outer corries of the Cuillins, 
Coire Labain is a good example of the large amount of material detached from the 
ridges by frost- weathering at a late epoch. On the slopes round its head are three or 
four large taluses, more or less confluent, the one from the gap between Sgiirr Alaisdair 
and Ssrurr Tearlach coming down some 1200 or 1300 feet to the floor of the corrie. 

It is perhaps significant that Coir' a' Grhrunnda, which lies in the heart of the 
highest mountains, and at a considerably higher level than its neighbours, has com- 
paratively little talus. We have seen that this valley differs from the others in having 
below it a large and well developed crescentic moraine. We may conjecture that the 
upper part of the Coir' a' Ghrunnda glacier survived after the heads of the neighbouring 
glens had been vacated, and that the moraine in this case corresponds with the taluses 
in the other corries. 

In conclusion, it should be remarked that frost and other subaerial agents have had 
no share in developing the characteristic forms of the mountains and valleys as described 
in the foregoing section ; their effect has often been to undo in some measure the work 
of ice-erosion, viewed from the standpoint of topographic forms. The slopes which hem 
in the cirques, for instance, have the familiar 'glaciated' surface far up towards the 
summit ridges, and it is these latter which have suffered from later destructive action. 
The boldly salient form and unbroken character of the ridges must have been more 
remarkable when they first emerged from the declining ice-cap than they are at the 
present time. 

* See Geol. Mag. 1899, pp. 485-491. 



252 ICE-EROSION IN THE CUILLIN HILLS, SKYE. 



EXPLANATION OF MAP. 

This sketch-map shows the central part of Skye on the scale of about i inch to a mile. The general 
character of the surface relief is roughly indicated by the contour-lines corresponding with altitudes of 
1000, 2000, and 3000 feet above sea-level. 

The doubly-barbed arrows indicate the movement of the ice during the stage of maximum 
glaciation, as deduced from the striated surfaces, the dispersal of boulders, etc. These arrows belong in 
the north-eastern corner of the map to the ice-sheet from the Scottish mainland, but elsewhere to the 
native ice-cap. In the Red Hills, which occupy much of the eastern portion of the map, the data are in 
general insufficient to determine the movement of the ice with any precision. 

The singly-barbed arrows given in several parts of the map indicate the movement of the native ice 
-during the later stages of glaciation, when the disturbing factor of the Scottish ice-sheet was removed. 

Certain lines drawn on the map are explained as follows : — A A A is the mid-stream-line of the Glen 
Sligachan ice-stream. Among the boulders in the drift, granite preponderates over gabbro to the right of 
this line and the reverse to the left. B is the corresponding line for the surface erratics, belonging to a 
later stage of the glaciation ; in Glen Sligachan itself this line is practically coincident with the preceding, 
but diverges from it at Sligachan Bridge. C C is the western limit of granite boulders carried by the 
southward-moving ice. D D is the northern limit of peridotite and picrite boulders from Coir' a' Ghrunnda 
and An Sgiiman. E is the moraine of Coir' a' Ghrunnda. 



3r 



Roy. Soc. Edin. 



Vol. XL. 



ICE EROSION IN THE CULLIN HILLS, SKYE. 




( 253 ) 



XIII. — The General Form of the Involutive 1-1 Quadric Transformation in a 
Plane. By Charles Tweedie, M.A., B.Sc. 

(Read 15th July 1901.) 

§ 1. In a communication read before the Society, 3rd December 1900, Dr Mum dis- 
cusses the generalisation, for more than two pairs of variables, of the proposition that : If 

then 

i=(f-x)/(l-xy); r,={x*-y)l(l-xy). 

If we interpret (x, y) and (£, >?) as points in a plane, it is manifest that the transfor- 
mation thereby obtained is a Cremona transformation. It has the special property of 
being reciprocal or involutive in character; i.e., if the point P is transformed into Q, 
then the repetition of the same transformation on Q transforms Q into P. Symbolically, 
if the transformation is denoted by T, T(P) = Q, and T(Q) = T 2 (P) = P ; so that T 2 = 1, 
and T = T -1 . Moreover, if the locus of P (x, y) is a straight line, the locus of Q (£, >;) is 
in general a conic. 

§2. The object of this note is to find the most general bilinear transformation con- 
necting two points (x,y), (£, v) of the form 

L 2 £+M 2 >7 + N 2 = 0j ' 

(Lj, etc., being linear functions of x and y) which possesses this property; i.e., the 
most general 1-1 transformation which is involutive in character and in which to a 
straight line corresponds a conic. 

This problem has already been discussed by Czuber (Monatshefte fur Mathematik 
und PhysiJc, 1894), but unfortunately his discussion is not free from error, and one 
of the best-known transformations of the kind — the so-called Hirst transformation — 
entirely escapes his observation. Moreover, he describes the above transformation (I.) 
as the most general 1-1 point transformation, which is by no means the case, as it is 
not difficult to frame 1-1 point transformations in which to a straight line corre- 
sponds a curve of higher degree than the second (v. Salmon's Higher Plane Curves). 
In his paper, however, he discusses a very large variety of degenerate cases, and this 
enables me to dispense with these entirely and to discuss only the leading case in 
which to a straight line corresponds a conic. 

^3. The transformation (I.) would appear to be the most general 1-1 quadric 
transformation. On solving for £ and >j we deduce 



f- 



L X M 2 - L 2 M 1 

_ N 1 L _-N,L 1 

VOL. XL. PART II. (NO. 13). 2 P 



254 MR CHARLES TWEEDIE ON THE 

The conies MjN 2 — M 2 'S 1 = ; NjLg - N 2 L 2 = ; L x M 2 - L 2 M. 1 = have three points 
in common, and this is the characteristic of the quadric Cremona transformation (v. 
Salmon). 

Conversely, any three conies having three common points may be so represented. 
Let ABCPQ, ABCQR, ABCRP be three such conies (where no two of the 
points P Q R are coincident). Let L x - 0, L 2 = denote two lines through P ; M x = 0, 
M 2 = two lines through Q ; N x = 0, N 2 = two lines through R. 

The conic ABCPQ may be represented as the intersection of corresponding rays 
of the pencils 

L x -aL., = 
M x - a M 2 = 0. 

Similarly, the conic ABCQR may be obtained from 

Mj-aM^O 
N 1 -aN 2 = 0, 

Nj and N 2 being lines suitably chosen through R. 
Now the two pencils of lines 

L.-aU = 

N.-aN^O 

furnish a conic which clearly passes through A, B, C, also through the centres P and R, 
and therefore through the five points ABC PR, i.e., they furnish the conic ABC PR. 
The values of a corresponding to A, B, C are found by expressing the condition that the 
three equations in x and y 

L^-aL^O; M x -aM 2 = 0; 1^-aN^O 
be consistent. When the cubic for a has two equal roots, two of the points coincide 
and the conies have contact of the first order ; when all three roots coincide the conies 
have contact of the second order — all at a common point. A point P may also coincide 
with A, say, in a given direction, but Q cannot coincide with A at the same time. 

It may be noted that a linear construction for any number of points on the third 
conic is hereby indicated, the first two conies being given. Let S be any point on the 
first conic, and let Q S meet the second conic in T. Then R T and P S intersect on the 
third conic in U. 

§ 4. Let the bilinear equations in x, y, £, >; be 

( 1 ) HAjX +B 1 ij+C 1 ) + , ] (A.^ + B,t/ + C 2 ) + A 3 x + B. iV + C 3 = 

(2) ^a^ + foy + yj + v (a.yX + ft0 + y. 2 ) +a s x+8& +y s = 0. 

If these equations are iuvolutive, then the interchange of £ and cc, >] and y, must 
give two equations which lead to identical solutions with (1) and (2). Hence the result 
of the substitutions must be to replace (1) and (2) by two equations, 

7<1)+Z(2)=0 

m(l) + v(2) = 
where kn — lm is distinct from zero. 



INVOLUTIVE 1-1 QUADRIC TRANSFORMATION IN A PLANE. 255 

The transformed equations are 

(1)' a<A 1 £+B l9 +C 1 )+y(A 8 £+ B 2 ^ + C 2 ) + A 3 f + B aV + C S = 
(2)' x(a 1 g+ etc. )+ etc. =0. 

Case 1. If 

(2) s (2)' 

there must exist the following equations in the coefficients of ( 1 ) — 

A 1 = A 1 , A, = B V A 3 = C 1; 
B 1 = A 2 , B 2 — B 2 , B 3 = C.„ 

C 1= A3, c 2 = b 3 , c 3 =c 3 , 

so that (1) may be written as 

I. K x £+ ^m + C 3 + G& + + C 2 (y + r}) + \{£y + x v ) = 0. 
But if A-! = B 1 = C± = 0, we may reverse signs throughout and deduce 

II. G 1 (x±£) + G 2 (y±ti) + B x (^±^) = 0. 

Similar results hold for the second equation. (I. is practically the only case dis- 
cussed by Czuber.) 

Case 2. Nothing new is gained by supposing 

(1)' S ±(2); (2) s ±(l). 
For the solutions of (1) = and (2) = are those of 

(l) + (2) = 0; (l)-(2) = 0, 
and the transformation transforms these latter equations into themselves, so that there 
is a reduction to the preceding case. 

Case 3. More generally, no new result is obtained by supposing 

(l)' = k(l) + l(2) (i.) 
(2)' s m(l)+ % (2) (ii.); 

for, since the repetition of the transformation gives again (l) = and (2) = 0, there 
would result 

(1) = k{k{l) + l(2)} + l{7n(l) + n(2)} 

(2) ^ m{k(l) + l(2)} +n\m(l) + n(2)} 

i.e., 

(Y) = {W+lm)(l)+l{k+n)(2) 
(2) = m(k + n)(D + (lm+n 2 )(2), 

giving 

k 2 + lm = l\ 
l(h+n) = ..... 

lm + n 2 =l ' 



m(k+/i) = y 
If ?=f=0, -m=h0, these equations reduce to 



256 MR CHARLES TWEEDIE ON THE 

Now it is possible to determine a and b such that 

a{k(l)+l(2)}+b{m(l)-k(2)}=a(l)+b{2), 

a'{k{l) + l(2)} + b'{vi(l)-k(2)}=-{a'(l) + b'(2)}; 

for these lead to 

ak + bm = a \ , . . a'k + b'm = —a' } ,r>\ 

al-blc=br } ' a'l-b'k=-b'r h 

pairs of equations which are consistent, since k 2 + Im = 1. Also —f can not be equal to . r 

Hence the original equations may be replaced by 

a (l)+6(2) = 

a'(l) + b'(2) = 0, 

so that the discussion again reduces to that of Case (1). 

§ 5. If Z = 0, m = 0, then k = ±1 ; n = =hl, a case already discussed. 

If Z=j=0, m= 0, there result, when k= +1, 

(l)=(l) + /(2) 
(2)= -(2). 

From the identity (2)'= — (2) it follows that (2) has the form 

x— g + K(y — >/) + L(s;j; — yg) = 0, (K and L constants). 

The other identity leads to 

£( A^x + B# + C x ) + }] ( A 2 x + B 2 y + C 2 ) + A. A x + B 3 t/ + C 3 
^x(A,i+ B lV +C 1 ) + l[x- i+ K(y - ,,) + U(xq - yg)]. 

The comparison of coefficients shows that the corresponding equation is 

(1) g(A 1 x+B 1 y+CJ+*i(B 1 x+B0+C 2 )+C 1 x+C 2 y+C 3 +l{lMv+x+Ky) = O; 

while (2) is 

Now, so far as solutions of (1) and (2) are concerned, 

x + Ky + La;,, = g+ K,, + Lyg 

= h { * +£+ K(y + n) + U%>i + vB}- 
Therefore for (1) may be substituted 

i(A,x+ .... )+etc. + |[z+£+K(y+^)+L(^+yf)] = 0, 

an equation collaterally symmetrical in xy | fy, and therefore of a type already discussed. 
Finally, if Z=|=0, m = 0, k= — 1, we obtain 

(iy=-(i)+«(2) 

(2)'= +(2), 
the solutions for which are the same as for 

(1)-A( 2 ) = 

(2) = 0, 

which are of a type already discussed. 



INVOLUTIVE 1-1 QUADRIC TRANSFORMATION IN A PLANE. 257 

§ 6. The analysis therefore leads to the conclusion that when the transformation is 

involutive the bilinear equations may be reduced to one or other of the types I. and II. 

If we consider (£, >?) as a fixed point, the equation I. is simply its polar with respect 

to the conic 

A 1 x 2 + 2B 1 xy + B$ 2 + 2C,x+ 2C,?y + C 3 = ; 

whereas the equation 

Cl ( x -£) + C 2 (y - V ) + B x (& - xn) = 

C 2 (V 



is simply the equation to the straight line joining (£, n) to the fixed point . 

V bj £>! 

Hence the theorem : — 

The most general transformation of the nature of a quadric inversion, in which to a 
straight line corresponds a conic, may be obtained as a point transformation in ivhich :— 

First. — To a point corresponds the intersection of its polars with respect to two 
fixed conies ; or 

Second. — To a point corresponds the intersection of its polar with respect to a 
fixed conic with the straight line joining the point to a fixed point. 

The case in which there are two equations of the form II. simply corresponds to the 
identical transformation. Naturally there are various degenerate cases, for many of 
which Czuber's paper may be profitably consulted. The ordinary inversion is a 
particular case of the second transformation in which the conic is a circle, while the 
fixed point is its centre. 

Both transformations have already been discussed geometrically, the first by 
Beltrami in 1863, in his well-known memoir, " Intorno alle coniche di nove Punti" 
{Mem. della Acad, di Bologna, Tomo II.) ; the second by Hirst (" Quadric Inversion of 
Plane Curves," Proc. R. S. L., 1865). 

Hirst never mentions the Beltrami transformations, although Beltrami had already 
shown how to obtain certain Hirst transformations, such as the ordinary inversion. 
Czuber (I.e.), in his analytical discussion, has omitted the Hirst transformations entirely. 

§ 7. The two transformations present several points of contrast, and that of Beltrami 
would appear to be the more symmetrical. 

In the Beltrami transformation let the two conies be represented by 

ax 2 + if +cz 2 = 
lx 2 + my 2 + nz 2 = Q, 

as referred to their common self-conjugate triangle X YZ. 
To any point (£, *j, ^) corresponds the point given by 

ax£ -f bytj +cz£ =0 
lx£ + myr\ + nz^ — , 
therefore 

x :y :z = (hu — cm)t]g : (cl — an)££ : (am — &/)£"»; 
and similarly 

£:iy.^—(bn — cm)yz: etc. : etc. 

There are four self-corresponding points, the points A, B, C, D, in which the two 



258 ME CHARLES TWEEDIE ON THE 

conies cut, so that X, Y, Z are the intersections of pairs of opposite sides of this 
quadrangle. 



To a straight line 



.-^ 



px + qy + rz — 




corresponds the conic 

*Z.p(bn — cm)>]£ = 0, 

i.e., a conic through the principal points X, Y, Z. This conic is not degenerate unless 
a coefficient is zero. (This would always happen if b/c = m/n.) 

If £> = 0, i.e., if the line passes through X, the conic breaks up into the line YZ 
(which corresponds to X) and a line through X. Thus, if to the point P corresponds 
P', to X P corresponds X P', and inversely ; so that the lines through a principal point 

X are paired in involution, the two self-corresponding lines 
of the involution being simply the two sides of A B C D 
that pass through X, viz., AB and CD. Any two corre- 
sponding lines through X are therefore harmonically separated 
by XABandXDC. 

If a line X P cuts B C in P, the ray X P' corresponding to X P therefore cuts B C in 
P', which is the harmonic conjugate of P with respect to B and C. Hence Beltrami's 
theorem : To a straight line not passing through a principal point corresponds a conic 
through the following nine points — the three points X, Y, Z, and the harmonic conjugates 
of all such points P in which the straight line cuts the six sides of the quadrangle 
ABCD. 

The discussion is simplified by noting that the conies of reference may be replaced 
by any two conies of the system through A B C D, and in particular by two pairs of 
opposite sides of A B C D, especially when all these points are real. 

Beltrami also proves that to a curve of degree n, passing a times through X, 
iS times through Y, y times through Z, there corresponds a curve of degree n' , passing 
a! times through X, /3' times through Y, y' times through Z, where 

il =2n ■ — a — ft — y ; 
nf — a — a — a ; n' — {3' = n — fi ; n! — y' = n — y ', 
ii. — 'In! — a' — fl' — y . 

One case is worthy of note. To a conic through two principal points corresponds 
a conic through the same points. If the conies intersect in P and P', P and P' are 
corresponding points and are coincident only when the conic passes through a vertex of 
A B C D, in which case the conies touch at that point. Hence any non-degenerate 
conic through two principal points and through two of the points ABCD must 
correspond to itself, for two conies cannot have four common points and contact at 
two of these points without coinciding. The points on such a conic are paired in an 
involution, and therefore the joins of corresponding points are concurrent, the centre of 
the involution being the intersections of the tangents at these two self-corresponding 
points through which the conic passes. 






INVOLUTIVE 1-1 QUADRIC TRANSFORMATION IN A PLANE. 259 

§ 8. In the Hirst transformation all points on the fixed conic are self-corresponding 
points, and the three principal points are X, the given fixed point, and the points of 
contact Y, Z of the tangents from X to the conic. To a straight line through X 
corresponds a line through X, but to a line through Y a line through Z, and vice versa, 
while the numerical equations for two corresponding curves are 

n' = 2n — a — (S — y ; 
n'-a' — n — a; n—fi' = n — y] n' — y=n — j3', 
n = In — a — /3' — y, 

so that the Beltrami transformation is the more symmetrical. 

In the Hirst transformation the points on any line through X are paired in an 
involution w r hich is hyperbolic or elliptic according as the line cuts or does not cut the 
fundamental conic. 

Also in order that a conic shall transform into a conic it must pass through two of 
the points X, Y, Z. Hence, if a conic transforms into itself it must pass through the two 
points Y and Z, for to a conic through X and Y corresponds a conic through X and Z, so 
that, if self-corresponding, it would pass through X, Y, Z, which is impossible. 

If the self- corresponding conic through Y and Z cut the fundamental conic again 
in P and Q, since P and Q are self-corresponding points, it follows that X P and X Q are 
tangents to the new conic. The points on it are paired in involution, the centre of 
involution being, of course, the point X. 

§ 9. If we take the fundamental conic to be 

x 2 — yz = 

it is easy to prove that the correspondence gives 

1 1 1 
y £ £ n 

and the self-corresponding conies are given by 

x 2 + yz + x(By + Gz) = 0. 

There are therefore a two-fold infinity of such conies. Such a conic is over-specified, 
for it passes through Y, Z, P, Q, and is tangent to X P and to X Q. This suggests the 
following theorem : — 

" If two conies cut in four points Y Z P Q, and if the pole of Y Z Avith respect to one 
conic is on the tangent at P to the second conic, it is also on the tangent at Q to the 
second conic and is the pole of P Q with respect to the second conic." 

This proposition may be verified analytically as follows : 

Let x 2 — ayz = be the equation in trilinear co-ordinates to one of the conies, so that 
the pole of x = with respect to it is the point X. 

Let P Q be the line 2x + By + Cz = 0. 

The equation to any conic through the four points is 

k(x* - ayz) + x( 2* + By + Gz) = 0. 



2()0 Mil CHARLES TWEEDIE ON THE 

Let (£, ij, £) be the co-ordinates of P. The equation to the tangent at P is 

'(i'/,f+^+B, y + CO-l-.y(etc.) + <etc.) = 0. 

Hence, if this line pass through X, 

hut 2£+B,+C£=0 

.-. 2Af+2£ =0 

Hence & = —1, and the conic has for equation 

x- + ayz + x(Ey + Cz) = , 

while there is no distinction between the points P and Q. The theorem is therefore 
established. Various sub-cases arise according to the relative positions of the four 
common points. 

The tangents at Y and Z to the second conic are given by 

az+Bx=0 (1) 

ay + Cx = Q (2), 

and the tangent at P to the first conic is 

2zg-ay£-az 1] = (3). 
These tangent lines are concurrent, provided 

which is the case. 

Hence the theorem : — 

" If two conies cut in Y, Z, P, Q, and if the pole of Y Z with respect to the first 
conic coincides with the pole of P Q with respect to the second conic, then the pole of 
Y Z with respect to the second conic coincides with the pole of P Q with respect to the 
first conic." 

Naturally both statements admit of reciprocation. In a sense, they are particular 
cases of the theorem that the eight tangents to two conies at their common points in 
general envelop a curve of the second class. 

£ 10. It may be noted that one of the three canonical forms of the 1-1 quadric 
transformation, as given in Miss Scott's Modern Analytical Geometry, 

_ 1 . 1 . 1 
i 'i i 
is a Beltrami transformation and not really a Hirst transformation. 
It corresponds to 

so that (;/■, y, z) is the point of intersection of the polars of (£, 77, £) with respect to tin' 

two degenerate conies 

x 2 -y 2 =0; ^ 2 -^ = 0. 

The other two are Hirst transformations. 



& 



INVOLUTIVE 1-1 QUADRIC TRANSFORMATION IN A PLANE. 261 

§ 11. Numerous examples of either transformation are to be found in the elementary 
geometry. One example of each is given. 

If the base A A' of a triangle A A' C is kept fixed, the orthocentre P of the triangle 
is such that C is the orthocentre of the triangle A A' P. Hence to C corresponds P and 
to P the point C. Moreover, if C moves in a straight line, the locus of P is in general 
a conic. The transformation is therefore one of the kind in question. 

Take A A' as the cc-axis, so that A and A' are the points (a, 0), ( — a, 0). Let C 
be the point (£, rj) ; then P has for co-ordinates 

Hence the two pairs of co-ordinates are connected by the relation 

x— £=0; yt]+x£—a 2 = 0. 

Hence the straight line C P passes through the point at infinity in a direction 
perpendicular to A A', and P is on the polar of C with respect to the circle whose 
diameter is A A'. Hence the transformation is a Hirst transformation. 

The analysis also leads to the known proposition that the three lines found by 
taking the polar of each vertex of a triangle with respect to the circle which has for 
diameter the opposite side are concurrent in the orthocentre of the triangle. 

§ 12. A Beltrami transformation is furnished by the following theorem of Professor 
Chrystal's, and its generalisation, viz. : " A circle meets the side B C of a triangle 
A B C in D and D', C A in E and E', and A B in F and F'. If A D, B E, C F be 
concurrent, then A D', B E', C F' are also concurrent. 

Tins is included in the following : P and P' are two points taken in the side A of 
the triangle A B, and Q Q' on the side B such that P.O F = p, Q.O Q' = <r, where 
p and a are constants. A Q and B P meet in S ; A Q' and B P' meet in S'. If A B is 
met by S in R and by S' in R', it follows that the six points P P' Q Q' PR' lie on 
a conic. Moreover, to S corresponds a unique point S' and inversely to S' corresponds 
S, so that the transformation from S to S' is involutive. Also if S move on a straight 
line S' in general traces out a conic. The transformation ought therefore to be either 
a Hirst transformation or a Beltrami transformation. 

To obtain the transformation, let OA and OB be taken as axes, and let A = a, 
B = b, P = a, Q = /3 (so that a and /3 vary). 

Then A Q and B P have for equations 

a & I (i.) 



Hence, if S be the point (x, y), 



a = 






bx n ay /•• x 



b—y' a — x 

VOL. XL. PART II. (NO. 13). 2 Q 



262 Ml! CHARLES TWEEDIE ON QTJADRIC TRANSFORMATION. 

Similarly if S' be the point (£, rj), 



■P~r/ ■ P = * — ( 11L ) 

' at an v 



b — y bi; a—x an 

i.e., 1^-pQ>- y Xb-i) = 0]a*to-a(a-i)(a-v)=Q. (v.) 

Hence (x, y) is the point of intersection of the polars of (£, n) with respect to the 
two degenerate conies : — 

BV _ p ( & _ y y = o ; a y - <r(a - xf = 0. (vi.) 

These conies determine a quadrilateral XYZW, which is such that the intercepts cut 
off hy its sides on A and B are bisected at 0, while the two pairs of lines pass 
through A and B respectively. For these conies may be substituted any two conies 
through X Y Z W. 

Two of the principal points are A and B. The third principal point is not 0, but 
the intersection C of X Z and Y W which are given by 

; cV(/o<r - a"-b 2 ) - ifp{pcr - a 2 b 2 ) - 2a po -<> - b 2 )x + 2bpa(p -a 2 )y + p(r (a?<r - b 2 p) = 0. 

(ABC is the self-conjugate triangle of the system of conies.) 
The lines through the origin parallel to these are given by 

xV- y 2 p=0. 

They are therefore parallel to the sides of the parallelogram K L M N, where 
KLMN are the points in which OA and OB are cut by the sides of XYZW. 
Hence the third line-pair X Z and Y W are such that each makes on the axes 
intercepts the square of whose ratio is p : cr. When p = <r, i.e., when the circles of 
inversion coincide, the parallelogram is a rectangle, and each line of the third line-pair 
makes equal intercepts on the axes. 

In the transformation as a Beltrami transformation the point has no important 
role. In the general Beltrami transformation the lines through B are paired in involu- 
tion, and they therefore determine a point-range in involution on any straight line 
such as A. Similarly, the lines through A determine an involution on B, and we 
have here the particular case in which the centres of involution of the point-ranges 
coincide in the point common to the two ranges. If A and B are real, and if L N pass 
through B, the locus of its middle point is a conic passing through A, and similarly 
for as the middle point of K M through A. Hence when A and B are real there 
may exist real points in finite number possessing the property in question. 

The transformation suggests the apparent generalisation : — A and B are fixed points 
in the plane of two involutive point-ranges P P' and Q Q', where P P', Q Q' denote 
corresponding points of the respective involutions. The lines joining A and B to 
PP' and QQ' determine a quadrilateral STS'T' in which S corresponds to S' (or T to 
T') in a 1-1 involutive quadric transformation. 



( 263 ) 



XIV. — Apparatus for Measuring Strain and Applying Stress, with an Account of some 
Experiments on the Behaviour of Iron and Steel under Stress. By E. G. Coker, 
D.Sc. Communicated by Dr C. G. Knott. (With Eight Plates.) 

(Bead 3rd June 1901.) 



CONTENTS. 



PAGE 

I. Introduction, 263 

II. Description of the Apparatus — 

1. Instrument for Measuring Strains, . 264 

2. Machine for applying Torque and 

Bending, 267 

3. Apparatus for applying Torque and 

Tension, 268 

III. Method op Experimenting, . . . 270 

IV. The Form of the Stress-strain Curve, 270 
V. The Form of the Curve at the Yield- 
point, 270 

VI. Recovery of Elasticity with Time, . 271 
VII. The Position of the Yield-point as 

affected by previous Stress, . . 277 
VIII. Twist in alternately opposite Direc- 
tions, 277 



IX. The Influence of Tension on Torsion — 

1. Tension within the Elastic Limit, and 

Torsion within the Elastic Limit, 

2. Effect of Tensional Stress on the 

Yield-point, .... 

3. Tension beyond the Elastic Limit, 
X. Effect of Torsion on Tension, 

XI. Effect of Bending on Torsion, . 

1. Bending within the Elastic 

and Torsion within the 
Limit, 

2. Bending beyond the Elastic Limit, 

3. Effect of Bending upon the Yield 

point, 

XII. Effect of Annealing, . 



Limit, 
Elastic 



page 

280 

282 
283 
285 

285 

286 
286 

288 
291 



I. — Introduction. 

The behaviour of metals under stress has long been the subject of investigation, 
both by mathematicians and physicists, so that the laws of strength are tolerably 
complete. Owing to the importance of iron and steel in construction, these materials 
have been subjected to very extensive tests, particularly in simple tension and com- 
pression. 

Numerous tests of cylindrical iron and steel bars in torsion are also available, the 
bulk of these being tests to destruction of samples of material used in actual machines 
and structures designed by engineers. In such tests scientific accuracy is not of much 
importance, the chief consideration being the obtaining of sufficient data for use in 
design. The most accurate torsional work upon iron and steel has been the work of 
physicists, and nearly all their investigations have been conducted upon specimens of 
very small sectional area ; the reasons for this, no doubt, being that such specimens in 
the form of wires are easily obtainable, and of great uniformity in size and quality, while 
large test pieces are costly to prepare, and, moreover, cause considerable difficulty in 
testing, because of the magnitude of the forces involved. Owing to the mode of manu- 
facture, the physical properties of wire often differ to a considerable extent from turned 

VOL. XL. PART II. (NO. 14). 2 R 



264 DR E. G. COKER ON 

specimens of iron and steel. These differences may be caused by the hardening effect 
of the drawing, minute cracks in the wires, want of roundness, and the like. It there- 
fore appeared probable that experiments on the lines indicated by physicists would be 
of some service, and it was with this idea that the investigation was commenced. 

The chief difficulty in the accurate investigation of the torsional properties of metal 
bars lies in the lack of suitable apparatus for the work ; and after reviewing the chief 
machines available for measuring strain and applying torque — to all of which there 
seemed some objection — it was resolved to design and construct special appliances for 
the work. 

Attention was first directed to the design and construction of a self-contained instru- 

O 

ment for measuring strains, which should be sufficiently accurate to measure strains of 
one second of arc ; and after some experiments an instrument was constructed which 
satisfied these conditions.* A modification of this was used in the work of this paper, 
and is described in Section II. 

In most machines for applying torque, the construction is such that the weigh-lever 
can only be used for torsion in one direction, and the ends of the specimen are fixed, 
so that it is impossible, for instance, to apply a bending moment and torque, or a 
tension and torque, together. 

A machine was therefore constructed to allow of torque in either direction, and also 
permit of the application of a uniform bending moment and a pure torque, to give a 
combined stress. A separate device was constructed for giving the combined stresses 
of tension and torsion. 

IT. — Description of the Apparatus. 

1. Instrument for Measuring Strains. 

In making measurements of small strains it is a great advantage to use an instru- 
ment which will read directly, and which is self-contained and wholly supported on the 
specimen under test, thereby avoiding external scales, the positions of which with respect 
to the specimen may be changed by a disturbing element, such as slipping of the grips, 
applied bending moment, and the like. In order to meet these conditions, an instrument 
was designed for the purpose of these experiments, and is shown in sectional elevation 
by fig. 1 , and in side elevation by fig. 2. It consists of a graduated circle A mounted 
upon a chuck plate B, provided with three centring screws adjustable by hand. Upon 
the Vernier plate J, an arm carries an extension K, upon which is secured a frame X, 
carrying a thick wire P. The movement of the wire is observed by a reading micro- 
scope carried in the sleeve R of an arm S mounted upon the short cylinder C, which 
latter is gripped upon the test bar by screws L. 

The reading microscope has an eye-piece T provided with a glass scale, and a right- 

* Cokek, " On Instruments for Measuring Small Torsional Strains. 1 ' Phil. Mar/ , December 1899. 




APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS. 265 

angled prism is interposed between this and the objective W, so that readings can be 
easily taken. The tube Q is free to slide or rotate in its guide R, but, in order to 
readily focus the wire, this latter is carried in a frame X, pivoted upon the Vernier plate 
J, and adjusted by a screw V. 

The microscope arm S is secured to the cylinder C by a divided collar, the two 
halves of which are pivoted on one side, and the free ends clamped by screws. 

If it is desirable to turn the telescope round or to release it altogether, the screw 
may be thrown out of engagement. Readings are taken from one edge of the thick 
wire, and as this edge is very distinct, it fatigues the 
eye much less than a spider line or scratch upon 
glass, which latter have the further disadvantage of being 
of appreciable thickness. Fig. 5 shows the appearance 
of the field of view of the reading microscope and the 
wire P. 

No appreciable error is caused by the fact that the 
divisions upon the glass scale of the microscope are 
linear measurements, while the movement of the wire is 
in a circle. For if ABC be the path of the wire and 
AC the chord, then the error is the difference between the arc ABC and its chord 
AC when the angle o( is a small quantity of the first order. 

I.e. ^A =r a -. 2r sin £L 

o fa a 3 a 5 \ 

m ( a 3 a 5 , * \ 

a small quantity of the third order, and therefore negligible. In practice this 
is shown to be the case, as no difference can be observed between the parallelism of the 
wire P and scale for any position of the former. The reading of the microscope scale 
may therefore be taken as directly proportional to the angular displacement, and the 
calibration is effected by moving the wire through a definite angle and noting the 
equivalent reading of the micrometer eye-piece. 

It is essential that the graduated circle be set accurately upon the bar, with its 
plane perpendicular thereto and its centre coinciding with the longitudinal axis of the 
bar. An arrangement was devised to effect this, consisting of a pair of divided collars 
a, the halves pivoted together at b, and secured by nuts c. The collars are wedge- 
shaped, in radial section to engage with correspondingly wide-angled grooves, upon 
the chuck plate and cylinder only the angled sides being in contact, so that the collars 
are readily fixed or freed when required. The lower halves d of the divided collars are 
connected by one or more distance pieces e, so that when the former grip their 
respective grooves each piece has one degree of freedom with respect to the clamp, and 



2G6 DR E. G. COKER ON 

this is sufficiently suppressed by the frictional grip of the collars, thereby causing the 
parts to act as one rigid whole for setting the instrument on the bar. 

Both main pieces are chucked by set-screws, and with a little experience this can be 
eifected as accurately as by self- centring chucks.* 

In nearly all machines for applying torque some bending is also present, and it is 
therefore necessary to eliminate any possible errors due to this cause. 

If the bar is bent in the plane containing its centre line and the observation wire, it 
has the effect of causing new parts of the wire to come opposite the scale, but no error 
in reading is caused thereby. If, however, the bar is bent in a plane a,t right angles to 
this, the effect of the bending will be read as an addition to, or subtraction from the 
twist. Bending in any other plane may be resolved into components in these two 
planes, and it is therefore only necessary to eliminate the error due to bending in a 
plane perpendicular to the plane of the paper. 

The error may be got rid of by using two reading microscopes set opposite to one 
another, and a mean reading taken, but as this doubles the labour of observation it is 
inconvenient. Another plan is to arrange the wire mid-way between the sections 
gripped by the set-screws : then if 

2a be the length under measurement, 
= angle of bending at first section, 
<p = angle of bending at second section, 

error in reading becomes a (sin 6 + sin </>) ; 

and if and <p are equal and opposite the error vanishes. A specimen stressed by two 
equal and opposite couples applied at its ends bends into the arc of a circle, and fulfils 
the necessary condition for the equality of and (p, and in the application of torque 
this condition has been fulfilled. As a matter of precaution the observation wire is 
always set in the plane of bending. 

In order to test the accuracy of the instrument, torsion tests were made (I.) with no 
bending, (II.) with bending moment of known amount. As an example the following 
may be quoted : — 

Turned bar of rivet steel . . Torsion arm= 15'00. 

Diameter 0*662 . . . Calibration. 

Length under test . . .1 min. = 54*4 divisions. 

* hoc. cit. ante. 



APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS. 



267 



Table I. 



Torque in 
inch lbs. 


No Bending 
Moment. 


Bending Moment 
480 inch lbs. 


Bending Moment 
800 inch lbs. 


Bending Moment 
1120 inch lbs. 


Reading. A 


Reading. A 


Reading. A 


Reading. A 



















-51 


-51 


-50 


-50 


7-5 


51 


51 


50 


50 




-51 


-50 


-51 


-50 


15-0 


102 


101 


101 


100 




-51 


-51 


-49 


-50 


22-5 


153 


152 


150 


150 




-51 


-51 


-50 


-51 


30-0 


204 


203 


200 


201 




-52 


-51 


-51 


-51 


37-5 


256 


254 


251 


252 




-51 


-52 


-50 


-51 


45-0 


307 


306 


301 


303 




-50 


-50 


-51 


-51 


52-5 


357 


356 


352 


354 




-51 


-50 


-52 


-50 


60'0 


408 


406 


404 


404 




-51 


-51 


-51 


-49 


67-5 


459 


457 


455 


453 




-50 


-50 


-50 


-50 


75-0 


509 


507 


505 


503 





2 


1 


1 


2 



The differences caused by bending will be discussed in Section XL 



2. Machine for applying Torque and Bending. 

The apparatus used for applying twist in either direction, and for the combined 
stresses of twist and. bending, is shown in side elevation by fig. 6, in plan by fig. 7, and 
in sectional end elevation by fig. 8. The machine was specially constructed for the 
work of this paper, and consists essentially of two similar and equal castings A, bored 
axially to receive double-coned spindles B, the outer ends of which project through the 
castings and are secured by nuts C. At the weigh-lever end the cone is secured to the 
casting by studs D, but at the other end, in order to take up the twist upon the speci- 
men, the cone is gripped partly by the back-nut C, and partly by a plate E pressed 
against its face by studs. 

Each casting is bored at right angles to the axis to receive arms F G, of which the 
former are used for hanging weights therefrom to give the torque, while the latter 
one, G, carries a link H, having an adjusting screw I, and nut J, whereby the weigh -levers 
F can always be brought to the horizontal position, the final adjustment being made 
with a sensitive level K '; while the other carries a balance weight L. The ends of the 



268 DR E. G. COKER ON 

specimen M under test are secured in grips N N upon the projecting ends of the 
cones B. 

In order to obtain a pure torque and a pure bending moment, both acting at the 
same time, each casting is supported by a ring (fig. 9) encircling the spindles B, and 
furnished with friction rollers P, running in grooves in the spindles B. The rings have 
bearings Q, turning in stirrups R, these latter being hung from a horizontal bar S, by- 
adjustable vertical hangers T. With this arrangement we get a pure torque of a known 
amount throughout the specimen. 

Bending Moment. — Into the outer ends of the nuts C are screwed projecting arms 
V, of known length and carrying weights at their ends. These put a bending couple 
upon the specimen without shear, the arm of the couple being the distance of the 
weight from the hanger T. With this arrangement simple twist and simple bending, or 
any combination thereof, can be applied to a specimen with ease. The specimen is free 
to take up its own position of equilibrium, since it is imperfectly constrained — (the 
specimen can be easily rocked about even when fully loaded, but always comes back to 
the first position after a few oscillations) — and the conditions of stress are accurately 
known. 

Corrections : Twist. — The results of tests on the friction of the roller bearing show 
that the friction is so small a quantity as not to introduce any sensible error. 

Bending. — The friction error is that due to the stirrups embracing the bearings Q, 
which latter were made large purposely. No experiments were made in which the 
bending moment varied during the experiment ; consequently it was sufficient in each 
case to calculate the error due to friction for the particular load applied, and to make 
the small corrections necessary. This has been clone in all cases. 

3. Apparatus for applying Torque and Tension. 

The apparatus for applying torque and tension is shown in general elevation by fig. 
11, and in plan by fig. 12. A detailed section of some of the parts with the measuring 
instrument fixed to the specimen is shown by fig. 13. 

The specimen A was screwed into a turned piece B, having a slotted hole above, 
and tapped to receive a screw C, centred in a corresponding depression in a piece of tool 
steel D resting upon a plate E, which latter was carried by four bolts F, depending from 
a cast-iron beam G mounted upon two pillars H. Below, the specimen was screwed into 
a turned piece J", carrying a sleeve and pulley L, the lower end of the piece being fitted 
to receive a nut M and hanger N for weights. The torque was applied by weights 
attached to fine bands made of clock spring steel, which latter were attached to the 
pulley at convenient points, and passed over guide-pulleys mounted on ball-bearings. 
The applied torque was balanced a,bove by a double-ended lever P, keyed to the piece 
B, so that its axis passed through the point of suspension, and the lever being furnished 
with screws at its outer ends, these latter pressed equally against the pillars H. The 



APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS. 



269 



weights used for applying the torque were made by Oertling, or were copies therefrom, 
and the twelve 200-pound weights for applying the tension were standard weights 
forming part of the equipment of the 100-ton Buckton testing machine in the laboratory. 
The method of suspension ensures that all the tension load is evenly distributed in the 
section of the specimen, and there is no correction for friction, 
as the load is a dead-weight one. 

In applying the torque a small correction must be made 
for the friction of the pulleys. This was determined as 
follows : — 

The pulley was first balanced by winding lead strips round 
its arms until it would stand in any position, or when rotated 
by a smart pull, continue to revolve several minutes. Next, 
equal weights, A B, were attached to the spring steel tape 
passing over the pulley with the ends vertical, and the additional 

mass required to just start the pulley in one direction was determined. The weights 
were then reversed, and the additional mass required was again determined, the mean 
value of the two being taken. 

Let Tj be the tension on one side. 




T, 



the other side. 



We have 



T 3 = tension horizontally. 
T ... 



T, 
T, 



e*2 



very approximately ; from which we get by a simple transformation, 

This value was calculated throughout the range. As an example the following 
numbers may be quoted for the left-hand pulley : — 



Table II. 



T : pounds. 


T 3 = VT 1 T 2 


T, pounds. 


T 3 =VT!T 2 


2 


2-0078 


12 


12-0118 


4 


4-008 


14 


14-012 


6 


6-0088 


16 


16-013 


8 


8-0095 


18 


18-014 


10 


10-0113 


20 


20-015 



The correction for the other pulley was slightly less. 



270 DR E. G. COKER ON 

III. — Method of Experimenting. 

The diameter of the bar to be tested was first ascertained by a micrometer caliper, 
the mean of several readings being taken. The measuring instrument was then applied, 
and the calibration value of the readings ascertained. The bar was then placed in the 
testing machine, and the balance weights adjusted to give zero torque. If bending 
moment had to be applied, this was effected before the final adjustment of the reading 
microscope, care being taken to bring the wire midway between the two sets of clamping 
screws, and also to set the wire in the most favourable position for taking accurate 
readings, viz., the plane in which bending takes place. Unless readings are taken at 
equal intervals of time, the time effect of a stress will show itself, and it is therefore 
very necessary that the separate loadings be at equal intervals. It was found that the 
most convenient interval was one and a half minutes, this being necessary to bring the 
weigh-beam back to its zero position ; and all readings were taken with this interval, 
except where otherwise stated. 

IV. — The Form of the Stress-strain Curve. 

Before taking up the detailed examination of the relation of stress to strain, it is of 
interest to consider the stress-strain curve as a whole. 

Fig. 15 shows the general nature of the stress-strain curve for a wrought-iron or 
steel bar of circular section when subjected to a gradually increasing torque. Starting 
from no torque, and gradually increasing the load upon the bar, the relation between 
stress to strain is found to be a linear one until near the point a, when the defect from 
linearity is first noticed in the gradual creeping up of the readings, the whole twist 
upon the bar being at the rate of from 1° to 2° per inch of length. 

At a the yield-point occurs, and there is a large increase in the strain, with no in- 
crease in the loading. The material has also changed from a nearly perfectly elastic to 
a semi-plastic condition, and the bar when released from load will no longer go back to 
zero, but shows a very considerable set. The material has also hardened by the process, 
and the curve rises at first quickly to a point c, and then more slowly until fracture 
occurs at d ; the strain then being generally considerably more than one hundred-fold 
the strain within the perfectly elastic condition. 

V. — The Form of the Curve at the Yield-point. 

The first sign of deviation from the linear law indicates the failure of the elastic state 
at the fibres most severely strained — viz., the outer ones — and a semi-plastic condition 
is entered upon, which, as the loading proceeds, extends inwardly until a more or less 
uniform shear stress is established throughout the section. The passage from the one 



APPARATUS FOP MEASURING STRAIN AND APPLYING STRESS. 271 

state to the other in a solid specimen requires a certain range of stress, so that the 
diagram at the point a exhibits a well-marked rounding. 

If we call q the maximum shear at the outer surface, 

r = radius of the specimen. 

r p = radius to which plasticity extends. 

Then the resistance of the bar to torque is the sum of the resistances due to ( 1 ) the 
still elastic core, (2) the semi-plastic shell, and may be represented by 



T = 27rq, 



o—l r' A dr + 2irq I r 2 dr 
J o J r p 



where v = any radius 



= 2 1 " 



up to the point where perfect elasticity prevails r = r p and 



but when the specimen is wholly plastic 

r P = 0, 
and we get 

which is ^ of the value at the elastic limit. 

It would therefore appear that if the bar changes from the elastic to the plastic 
condition at the yield-point, the maximum torque will be four thirds of that value at 
which the first-marked deviation from perfect elasticity occurs. 

The result of experiment shows a fair agreement with this conclusion. In the 
example of a wrought-iron specimen quoted in the next section, Table III., col. I., the 
first-marked deviation occurs below 375 inch pounds, while the material failed at 
525 inch pounds, giving a ratio of 1 "4. 

Taking another case for the steel specimen quoted in the same section, Table IV., 
col. I., the first deviation occurred below 675 inch pounds, and failure took place at 
870 inch pounds, corresponding roughly to a ratio of 1"29, which is very close to f. 

Having regard to the difficulty of observing exactly the first sign of failure, it seems 
probable that the conditions assumed are not far from the truth. 



VI. — Eecovery of Elasticity with Time. 

If a bar of iron or steel be subjected to a torque causing a permanent strain in it, the 
condition of the bar becomes quite different ; it no longer obeys Hooke's law, and the 
strain for a given stress is now greater than before the increase, being more marked 
at the higher loads. As an example we may take that of a turned wrought-iron bar 

VOL. XL. PART II. (NO. 14). 2 S 



272 



DE E. G. COKER ON 



of length between centres of 4*00 inches; diameter 0*472; calibration value of 
readings 1 min. = 12 "85 divisions. The following results were obtained : — 

Table III. 

Column I. 



Torque in inch lbs. 


Reading. 


A 








243 


75 


243 


243 


150 


486 


244 


225 


730 


242 


300 


972 


254 


375 


1226 


268 


450 


1484 


140 


480 


1624 


160 


510 


1784 




525 


Went off scale 





The load was now removed, and immediately afterwards re-applied, with the follow- 
ing result : — 

Table III. — continued. 
Column II 



Torque in inch lbs. 


Reading. 


A 








245 


75 


245 


255 


150 


500 


262 


225 


762 


269 


300 


1031 


289 


375 


1320 


249 


300 


1071 


249 


225 


822 


259 


150 


563 


265 


75 


298 


272 





26 





APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS. 



273 



It will be seen at once that the bar exhibits quite different qualities from that shown 
before. The stress is now no longer proportional to the strain, and the curve showing 
the relation between the two no longer returns upon itself, but forms a looped figure. 
Similar results are obtainable from bars subjected to tensional stress.* t 
If the bar be tested again after a short interval of time, recovery will be found to be 
very marked, At the end of one hour a test of the bar gave the results shown by 
column III., there being a marked falling off of the increments at the higher loads. 
Thus the strain caused by increasing the torque from 300 inch pounds to 375 inch 
pounds now caused only 272 units of strain, instead of 289 ; and similarly at the end 
of three hours we find a further decrease to 268 units. The recovery of the bar was 
tested at suitable intervals of time, as shown in the annexed table, the effect becoming 
less apparent as the time increased ; but practically perfect recovery was reached at the 
end of two days, and very little change was noticeable after this time. 



Table III. — continued. 
Column III. (One hour afterwards.) 



Torque in inch lbs. 


Reading. 


A 








246 


75 


246 


252 


150 


498 


255 


225 


753 


266 


300 


1019 


272 


375 


1291 


248 


300 


1043 


250 


225 


793 


257 


150 


536 


260 


75 


276 


269 





7 





The results may be shown graphically by direct plotting, but it is more convenient 
to adopt the plan of subtracting from each reading a number proportional to the torque, 
and plot the new set of readings thus obtained. The method is due to Prof. Ewing, 
and is used in fig. 16, the diminution in the case being 200 units of scale reading for 

* Ewing, " On the Measurement of Small Strains in the Testing of Materials and Structures." Proc. Royal Society, 
May 1898. 
t Muir, " On the Recovery of Iron from Overstrain." Phil, Trans., 1899. 



274 



DR E. G. COKER ON 



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APPARATUS FOP MEASURING STRAIN AND APPLYING STRESS. 



275 



a torque of 75 inch pounds. A time-recovery curve, fig. 17, has been plotted, the 
ordinates of which correspond to the reading under a torque of 375 inch pounds and 
the abscissae are times ; this curve shows in a marked manner how rapid is the recovery 
at first. 

As a means of comparison with, the last bar, a steel bar was now tested, the speci- 
men being classed as machinery steel, i.e., semi- mild. Length under test 4 "00 ; dia- 
meter 0*425 ; calibratioD 1 min. = 12*85 divisions. 

The following results were obtained : — 



Torque in inch lbs. 


Reading. 


Difference. 








385 


75 


385 


385 


150 


770 


387 


225 


1157 


386 


300 


1543 


387 


375 


1930 


393 


450 


2323 


387 


525 


2710 


393 


600 


3103 


400 


675 


3503 


420 


750 


3920 


311 


780 


4231 


444 


810 


4675 


254 


825 


4929 


380 


840 


5309 


700 


855 


6009 




870 


Went off scale 





The load was then removed, and again applied by increments of 75 inch pounds 
until a limit of 750 inch pounds was reached, the load being afterwards reduced by 75 
inch pounds to nothing. Tests were made at intervals of time, as recorded in Table 
IV., which latter shows that the recovery is much slower in the former case ; and even 
at the end of nineteen days the specimen showed signs of the initial overstrain. 

The curves, fig. 18, showing the results of the experiments were plotted by the 
indirect method previously described, 350 units being subtracted for an increment of 



276 



Dil E. G. COKER ON 



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APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS. 277 

75 inch pounds of torque. The rate of recovery is also shown by fig. 19, corresponding 
to fig. 17 of the former case. The readings at 750 inch pounds are plotted as ordinates, 
and the times as abscissae. The difference between these latter curves is very apparent. 
From the diagrams it is apparent that the bar recovers very rapidly at first like the 
wrought iron ; but this rate of recovery soon slackens and becomes less and less 
apparent as the time increases, and unless a very considerable time is given the 
recovery does not become complete (cp. Table XV., col. X.). 

VII. — The Position of the Yield-point as affected by previous Stress. 

The effect of a previous stress upon the properties of a bar has been explained in 
Section VI., and it remains to point out that overstrain in one direction has a very 
considerable influence upon the yield-point or curve, separating the elastic from the 
plastic stage ; in fact it disappears, but gradually reappears again — the recovery in the 
case of the iron being practically complete in two days, while for the steel nineteen days 
effects partial recovery only. In both cases, if sufficient time be given, the yield-curve 
will assume a definite position above the last position, and this rise is augmented by every 
overstrain. As an example, we may take that of a wrought-iron bar, having a length 
under test of 4 - 00 inches ; diameter 0'420 inches ; calibration 1 min. = 12*8 divisions. 

The bar was subjected to stress extending beyond the yield-point, and afterwards 
left to rest for a minimum period of 1-^ days, when the load was repeated. Eight 
tests were made, and each time there was a perceptible rise in the yield-curve. The 
observations were plotted with each curve spaced 1000 divisions from its neighbour. 
The curves are given in fig. 20, and require no further explanation. 

VIII. — Twist in alternately opposite Directions. 

C 

It has long been a common assumption that the limits of elasticity for a bar sub- 
jected to torsion lie equally distant from the position of no torque, and this is no 
doubt true for a specimen not previously strained. 

Apparently the first theoretical discussion of the problem is that by James 
Thomson,* and in his original paper he makes the further assumption " that the limits 
of elasticity in a substance which has already been strained beyond its limits of 
elasticity are equal on the two sides of the shape which it has when in equilibrium 
without disturbing force." This note, added in October 1877, goes on to say: "A 
supposition which may be true or may not be true. Experiment is urgently needed 
to test it, for its truth or falseness is a matter of much importance in the theory of 
elasticity." 

The paper further points out that these assumptions lead to the important result 
that if a wire be overstrained, its strength to resist torsion in the original direction is 
twice that in the other direction. 

* Cambridge and Dublin Mathematical Journal, 1848 ; and article "Elasticity," Enc. Brit. 



278 



DK E. U. COKER ON 



From the mathematical point of view, Thomson's conclusions may be arrived at as 
follows : — 

If a specimen be subjected to stress sufficient to cause a uniform shear throughout, 
and then be released, we have a new distribution of shear throughout the section, 
which may be expressed by 

Shear = q — o/r 
where q„ = original shear at the external radius. 
r = any radius. 
a = a constant. 
Since the bar is in equilibrium, we must have 



/: 



giving 



" (//„ - ar)2Trr 2 dr = O 



4 j. 

3 r»' 



Thus the shear in the bar is given by the expression 



4 r 




The distribution m.Sij be shown graphically, as in fig. 21, 
by a line AB, where OB = q and AC = 



3 



This line evidently crosses the axis OR at the distance 
3 
OE=-r, and gives a point on the circle of no stress. 

Clearly, if no change has taken place in the limits of 
elasticity, the maximum shear is q at the centre, and 
evidently the bar will now stand a torque given by the 
expression 



Fig. 21. 



T = 



4 So . /-, 4 r, 
o — r + q.\ 1 — o " 
.3 r„ x "\ 3 r 



2-jrrWr = g Trqji ; 



while in the opposite direction the torque will be given by the expression 



T= \ r " 



v>, 



q„ 



1 - 



4 r\ 



2-7rr 2 dr = 5 7rq ri . 



3 r '-*°V 3 rj_ 

It remains to be seen if the assumptions are justified. 

In order to examine this point, a wrought-iron specimen was taken, having a length 
under test of 4 - 00 inches; diameter 0*634; calibration value 1 min. = 12*76 divisions 
of the scale. 

The specimen was set in the machine so that torque could be applied in either 
direction, and observations were made of the strains for loads, which in turn caused 
permanent set in both the positive and negative directions. 

These readings are plotted in fig. 22, and from an inspection of this it is ap- 
parent that the stress-strain curve was approximately linear before the yield-point 



APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS. 



279 



was reached. The return curve was less so, but as soon as torsion was applied in the 
negative direction the linearity disappeared, and the strains, though irregular, became 
greater and greater as the torque increased. The material finally gave way under a 
torque of about 1100 inch pounds. The torque was now reversed, and the stress-strain 
curve became approximately linear until the zero torque was reached, from which point 
the curve began to bend over to the left, until a torque of 1175 inch pounds was reached. 
In order to roughly test the behaviour of the specimen still further, the applied 
torque was continued, but no strain measurements were taken. 



Toryjuue, lmjch> ^S 



DcslarGuTii 




sctocrc 



Each complete cycle produced a hardening effect on the bar, widening its limits of 
endurance each time until a final limit of 1750 inch-pounds of torque was reached after 
fourteen reversals of the stress. The bar was now cracked in several places along the 
minute seams of impurities, and further experiment seemed useless. 

This experiment demonstrates that the limits of elasticity do not remain in their 
original positions, and, further, it shows that stress carried beyond the elastic limit in 
one direction reduces the other limit to zero. The conclusion derived from the theory 
above, that the bar is twice as strong to resist torsion in the original direction as in the 
other, is also not borne out by the experiment. 

A second bar of wrought iron was next examined in the same manner, only four 
cycles being performed, of which the first two are shown in fig. 23 and the last two in 
fig. 24. These curves exhibit the same general properties as the one described above. 
It is evident from figs. 23 and 24 that, after the first reversal of stress, there is no perceiv- 
able yield -point, all such critical points being absent. The commonly received idea 

VOL. XL. PART II. (NO. 14). 2 T 



280 



DR E. G. COKER ON 



that raising the elastic limit in one direction lowers it in the contrary direction does not 
hold good here, since all critical points vanish. 

The further development of the idea that the distance apart of the limits is a con- 
stant, appears to have no phy sical basis for the torsion of iron. 



IX. — The Influence of Tension on Torsion. 

1. Tension within the Mastic Limit, and Torsion within the Elastic Limit. 

Among the notable experiments made upon the influence of tension upon torsion are 
those of M'Farlane upon steel pianoforte wire.* 

From the article it does not appear that any experiments were made to ascertain 
whether tension within the elastic limit has any influence upon torsion within the elastic 
limit, but in any case it was thought worth while to make the experiments, as speci- 
mens of much larger diameter could be dealt with. 

The first specimen tried had the comparatively large diameter of f inch, and the 
maximum tension load which could be applied was 3000 pounds. Repeated experiments 
failed to show any difference in the torsional properties of the bar, whether loaded or 
unloaded. 

A second bar was then prepared, having a diameter of \ an inch, and the experiment 
was repeated with tension loads varying from 200 to 3000 pounds, the latter corre- 
sponding to a stress of 15,300 pounds per square inch. The diameter of the pulley was 
41 '62 inches, so that a weight of one pound in each pan corresponded to a torque of 
41*62 inch pounds. 

The length of the specimen was 8 inches, and the calibration value gave one division 
of the scale =16*85 seconds. 

The following Table gives a summary of the results obtained : — 

Table V. 





Mean Value of Reading corresponding to 




Tension Load on 

Specimen. 

Lbs. 


1 lb. in each pair = 41 "62 inch lbs. 


Mean of Columns 
2 and 3. 








Torque increasing. 


Torque diminishing. 




200 


59-00 


58-98 


58-99 


600 


59-00 


58-74 


58-87 


1000 


58-56 


58-70 


58-63 


2000 


58-59 


58-70 


58-65 


3000 


58-75 


58-65 


58-70 



* Enc. Brit. Art. "Elasticity." 



APPARATUS FOP MEASURING STRAIN AND APPLYING STRESS. 



281 



As will be seen from the last column, the values obtained differ very little, in no 
case varying more than one-half of one per cent. 

The above experiments were carried out for me during the latter part of 1898 and 
the beginning of 1899 by Mr Colpitts — then a student in the Civil Engineering De- 
partment of the University. As a test of the accuracy of these results, a third bar was 
prepared, having a diameter of 0*375 inch; length 8 '00. A new objective was fitted 
to the measuring instrument, rendering it much more sensitive. The calibration value 
gave 1 minute of arc = 62 '4 divisions of the scale. This necessitated low torques, in 
order to prevent the observation wire from passing out of the field of view. A new pulley 
was used, having a diameter of 20'82 inches, and weighing with hangers, etc., 120 
pounds. 

A test was first made with no tension load beyond that of the pulley, and imme- 
diately afterwards a load of 2400 pounds was applied, corresponding to an increased load 
of 21,700 pounds per square inch. The readings obtained are shown in Table VI. 

Note. — Considerable difficulty was experienced in making accurate readings when the 
tensional load was applied, as the time of vibration of the heavy weights with respect 
to the specimen was so large that any accidental motion due to the putting on or taking 
off the weights was very difficult to damp out. 

A deep four-armed vane was attached to the hanger and dipped into a water-trough 
on the floor ; this effected a great improvement, but did not wholly counteract the 
vibration. The readings obtained in Table VI. show a slight diminution when a ten- 
sional load is applied, but owing to the difficulties of observation mentioned above, the 
author feels he cannot lay much stress upon them. The observations were repeated 
with very nearly the same result. As will be seen in the next section, bending affects 
the angular distortion in the same manner. 

Table VI. 





No Tension except Weight of Pulley. 


Tension, 2400 lbs. - 


t- Weight of Pulley. 


Load in each Pan 
in lbs. 




















Reading. 


Difference. 


Reading. 


Difference. 


0-4 





196 





194 


0-5 


196 


195 


194 


195 


0-6 


391 


195 


389 


193 


0-7 


586 


197 


582 


195 


0-8 


783 


196 


777 


196 


0-9 


979 


195 


973 


194 


1-0 


1174 




1167 





282 DR E. G. COKER ON 

2. Effect of Tensional Stress on the Yield-point. 

The only experiments upon the yield -point appear to be those of M'Farlane.* These 
showed that a tension lowered the yield-point. Reasoning from this result, Lord Kelvin 
concludes that a compression stress would raise it, but no experiments appear to have 
been made to verify this conclusion. 

In order to examine the effect of tension at or about the yield-point, a bar of wrought 
iron was taken and cut into two parts ; one specimen was turned truly parallel to a 
convenient diameter (0*424 inches), and the second was made exactly the same size. 
Both specimens were tested and found to be perfectly cylindrical, as far as could be 
ascertained by a micrometer gauge. 

The first specimen was then tested in the ordinary way, with the result shown in 
column I., Table VII. The first noticeable deviation occurred when each pan was 
loaded with a weight of 16 pounds — corresponding to a torque of 333 inch -pounds, the 
maximum torque being 385 inch pounds. 

The second bar was then stressed ; but before the tension load was applied a pre- 
liminary reading was taken — to see whether the readings agreed with those from the 
first specimen, and, as will be seen (col. II.), the agreement is very close. 

The specimen was now loaded with an additional 2400 pounds — corresponding to 
an increase of stress of 17,900 pounds per square inch — and a torque applied by incre- 
ments. As shown by column III., a slight deviation was noticed at 333 inch-pounds, and 
failure was accomplished by a torque of 360 inch-pounds. 

This result shows in a marked way the lowering of the yield-point by tension, and 
confirms M'Farlane's experiments. 

* Loc. cit. ante. 



APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS. 



283 



Table VII. 

Diameter, 0"424". Length, 4"00". 12'8 divisions of scale = 1 min. of arc. 



Load in each 


Column I. 


Column II. 






Pan. 


No Tension. 


No Tension. 


Lbs. 






Reading. A 


Reading. A 


2 










157 


155 


3 


157 


155 




155 


157 


4 


312 


312 




157 


156 


5 


469 


468 




156 


157 


6 


625 


625 




156 


156 


7 


781 


781 




154 


156 


8 


935 


937 




155 


157 


9 


1090 


1094 




157 


157 


10 


1247 


1250 




156 


157 


11 


1403 


1407 




156 


157 


12 


1559 

157 


1564 


13 


1716 

156 




14 


1872 

157 




15 


2029 

159 




16 


2188 

168 




17 


2356 

120 




17-5 


2476 

950 




18 


3426 

400 




18-2 


3826 




18-5 


"Went off scale 





Column III. 


Load in each 


Tension 2400 lbs. 


Pan 




Lbs.' 






Reading. A 


2 







156 


3 


156 




155 


4 


311 




156 


5 


467 




157 


6 


624 




158 


7 


782 




156 


8 


938 




156 


9 


1094 




157 


10 


1251 




155 


11 


1406 




158 


12 


1564 




158 


13 


1722 




156 


14 


1878 




156 


15 


2034 




81 


15-5 


2115 




106 


16-0 


2221 




120 


16-5 


2341 




472 


17-0 


2813 


17-3 


Went off scale 



The results of Table VII. are plotted and are shown on fig. 25. 

3. Tension beyond the Elastic Limit. 

A machinery steel bar turned to a mean diameter of 0'537, with a length of 8*00 
under test, was chosen. The bar was first placed in the torsion machine, and gave the 
results under test shown by col. I., Table VIII. The mean twist for 75 inch pounds 



284 



DR E. G. COKER ON 



was 278 divisions. The specimen was then set in the tension grips of the Buckton 
Testing Machine, and a gradually increased load applied, until a permanent set of - 18 
inches was produced. Immediately after, a fresh test in torsion was made, the results 
obtained being shown by col. II. The results are also plotted in fig. 26, from which 
it will be seen that the effect of the tensional overstrain has entirely altered the pro- 
perties of the material under torsion. The strain is no longer proportional to the stress ; 
the deviation being even more marked than in the case of specimens upset by a previous 
overstrain by torsion. 

Table VIII. — Steel Specimen. 

\ 

Diameter, 0"537". Length, 8 - 00". 12*75 divisions of scale = 1 min. of arc. 





Column I. 




Column II. 




No Tension. 




Specimen permanently lengthened 0"18 inch. 


Torque in 
inch lbs. 


Reading. 


A 


Torque in 

inch lbs. 


Reading. 


A 








278 








299 


75 


278 


279 


75 


299 


301 


150 


557 


278 


150 


600 


321 


225 


835 


277 


225 


921 


339 


300 


1112 


277 


300 


1260 


364 


375 


1390 




375 


1624 


406 








450 


2030 


484 








525 


2514 


612 








600 


3126 


292 








525 


2834 


298 








450 


2536 


300 






i 


375 


2236 


300 








300 


1936 


305 








225 


1631 


310 








150 


1321 


311 








75 


1010 


310 











700 








APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS. 



285 



X. — Effect of Torsion on Tension. 

The effect of torsion upon the properties of a bar subjected to tensional stress was 
only examined below the elastic limit. 

The measuring instrument used was of the Ewing type,* each unit of extension 
representing 50 o o inch upon an 8 -inch length ; diameter of bar, 0*498 inch. 

A series of tests were made, beginning with no tension and increasing by equal in- 
crements until the yield-point of the material was reached. The results are recorded in 
Table IX., and it will be seen that no difference was observable, whether the bar was 
twisted or not, provided the elasticity of the bar remained unimpaired. 

Table IX. 





No Torsion. 


Torque of 141 inch lbs. 


Torque of 282 inch lbs. 


Torque of 423 inch lbs. 


Loads. 
' Lbs. 




















Reading. A 


Reading. A 


Reading. A 


Reading. A 


200 
















15 


15 


16 


15 


400 


15 


15 


16 


15 




14 


15 


15 


16 


600 


29 


30 


31 


31 




14 


14 


15 


14 


800 


43 


44 


46 


45 




16 


15 


15 


15 


1000 


59 


59 


61 


60 




14 


15 


14 


15 


1200 


73 


74 


75 


75 




14 


15 


14 


15 


1400 


87 


89 


89 


90 




15 - 


14 


14 


14 


1600 


102 


103 


103 


104 




14 


15 


14 


14 


1800 


116 


118 


117 


118 




15 


15 


14 


16 


2000 


131 


133 


131 


134 




15 


14 


15 


13 


2200 


146 


147 


146 


147 




15 


14 


14 


15 


2400 


161 


161 


160 


162 



XL — Effect of Bending on Torsion. 

One of the most interesting cases of stress which occurs in practice is that of torsion 
combined with bending, a subject which has received little or no attention from the 
experimental side. The apparatus described in Section II. enables uniform twist and 
uniform bending to be applied to a bar in any proportions, and the torsional strain to be 
accurately measured without reference to any external body ; so that the bar can 

* On Measurements of Small Strains in the Testing of Materials and Structures. By J. A. Ewing, F.R.S. Proc. 
Royal Society, May 1895. 



286 



DR E. G. COKER ON 



assume its own position of equilibrium without affecting the readings of the measuring 
instrument. 

Attention has been directed to the influence of bending on the torsional properties 
of a bar. 

1. Bending within the Elastic Limit, and Torsion within the Elastic Limit. 

In a previous section it has been shown that the effect of a tension produced little 
or no effect upon the torsional properties of a bar while in the elastic state. It might 
be expected, therefore, that a bending action which results in a varying tension and 
compression upon the longitudinal fibres would have but little effect upon' the strain. 
As an example we may take the case quoted in Section II. of a rivet steel bar, in which 
an increase in the bending moment caused a slight diminution of the strain per unit 
torque. 

Similar decrements were found in every case of the same type ; as, for example, in 
the case of a semi-mild steel bar of diameter 0"869 inch, and of length 8'00 inches 
under test. 

The unit reading corresponds to -^ minute of arc. 

Table X. 





No Bending Moment. 


640 inch lbs. 


Torque in 
lbs. 


















Reading. 


Difference. 


Reading. 


Difference. 








166 





163 


75 


166 


166 


163 


164 


150 


332 


166 


327 


166 


225 


498 


165 


493 


166 


300 


663 


167 


659 


165 


375 


830 




824 





2. Bending beyond the Elastic Limit. 

A more interesting case was that of a steel bar in which the bending moment was 
gradually increased until a permanent set w r as given to the bar in the plane of bending. 
The readings obtained are shown in Table XL, and a summary of the results in Table 
XII. It will be noticed that when the bar is bent the true value of the torque is given 
by its apparent value multiplied by cos 6, where = angle of bending of the weigh- 
lever about its axis. 

The results show that the slight diminution in the readings within the elastic limit 
is followed by a much greater rise when the yield-point is reached. 



APPARATUS FOR MEASURING STPvAIN AND APPLYING STRESS. 



287 



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VOL. XL. PART II. (NO. 14). 



2 U" 



288 



DR E. G. COKER ON 



Table XII. 



Diameter of bar, 0*511". Length, 8'00". 54 - 7 divisions = 1 min. of arc. 



Bending Moment. 


Readings for Torque 
of 60 inch lbs. 


L. of Bending 
at Weigh-lever. 


Cos e. 


Corrected 
Reading 

= Reading 
x cos 0. 





1091 


0° 


1-000 


1091 


224 


1088 


30' 


•999 


1088 


337 


1086 


48' 


•999 


1086 


529 


1083 


1° 54' 


•999 


1083 


752* 


1084 


2° 24' 


•999 


1084 


922 


1090 


3° 10' 


•998 


1088 


1092 


1095 


3° 20' 


■998 


1092 


1432 


1105 


4° 30' 


■997 


1102 


1772 


1123 


7° 0' 


■993 


1115 



Permanent set due to bending. 



3. Effect of Bending upon the Yield-point. 



The experiment was performed in a similar manner to that in Section IX. Two 
bars cut from the same rod were turned up to exactly the same size. One of them was 
tested in the ordinary manner, and the other was subjected to bending moment below 
the elastic limit, and then twisted beyond the yield-point. Each bar was 0*489 inch 
in diameter, the length under test being 4 inches, and 12 '8 5 divisions on the scale 
corresponded to 1 minute of arc. The readings are recorded in Table XIII., in which 
column I. refers to the first specimen, and the remaining columns to the second 
specimen. The readings in column II. were made to check the correctness of the 
setting of the measuring instrument. The readings show a remarkable lowering of the 
yield-point for a bending moment of 668 inch pounds ; the reason for which was not at 
first apparent, until it was noticed that the specimen took a permanent set, the ends 
being bent to a considerable degree. 

At first sight this might appear to be a mere time effect ; but in the author's opinion 
the probable cause was the increase of stress, due to the torque applied later. Appar- 



APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS. 289 

ently the maximum stress due to bending was of itself insufficient to cause yield, 
but the application of a further torque caused the principal stresses to assume the values 



A=f +y# +s ! 



^-v/f + ? ! 



2 V 4 

where p n = normal stress due to bending. 

q = shear stress due to applied torque. 

If we adopt Rankine's theory of maximum stress, then p x in this case passed the 
working limit of the material, and a set resulted. 
On the maximum strain theory of St Venant, 

if e x = principal strain, 
m = Poisson's ratio, 
then 

in 

m — 1 . m + 1 



and since m has a value between 3 and 4 for steel, it is clear that the addition of a 
shear stress q would cause an increase in the value of e, which, if below the limit before, 
might increase sufficiently to cause failure. 

The relation of stress to strain after the permanent set is clearly shown by a further 
test indicated in the table, column IV. There is now considerable hysteresis in the 
relation of stress to strain. 



290 



DR E. G. COKER ON 



Table XIII. — Combined Bending and Twist. 



Bar I. 




Bar II. 








Col. I. 


Col. II. 


Col. III. 


Col. IV. 




No Bending 


No Bending 




Bending Moment 




3 hours after 


Torque 


Moment. 


Moment. 


Torque 


668 inch lbs. 


Torque 


last Test. 


in inch 






in inch 
lbs. 




in inch, 
lbs. 




lbs. 








Reading. A 


Reading. A 




Reading. A 




Reading. A 

























195 


196 




196 




201 


75 


I 95 


196 


75 


196 


75 


201 




195 


196 




196 




202 


150 


390 


392 


150 


392 


150 


403 




197 


193 




198 




207 


225 


587 


585 


225 


590 


225 


610 




197 


197 




215 




208 


300 


784 

196 


782 


300 


805 

765 


300 


818 

266 


375 


980 

125 




375 


1570 


375 


1084 

194 


420 


1105 




After 2 m 


inutes, went off 


300 


890 




44 




sea 


le entirely 




201 


435 


1149 

42 








225 


689 

203 


450 


1191 

42 








150 


486 

202 


465 


1233 

43 








75 


284 

208 


480 


1276 

46 
1322 











76 


495 












46 










510 


1368 

50 










525 


1418 

50 










540 


1468 

48 










555 


1516 

62 










570 


1578 

98 










585 


1676 

700 










605 


2376 

1100 










615 


3476 













The author has not been able to find any other experiments bearing upon the 
position of the yield-point as affected by bending. The yield-point is, however, known 
to be lowered by tension, as mentioned previously. 



APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS. 291 

A case which bears considerable resemblance to the case of permanent set last 
quoted is one by M'Farlane,"* who has shown that if a wire is twisted to nearly its 
limit of torsional elasticity, an increase in pull will cause the torque to give the wire a 
permanent set. This latter case can be easily explained in the same manner as the 
one described above. 

XII. — Effect of Annealing. 

It has long been known that iron and mild steel stressed beyond the limit of elasti- 
city regain their elastic properties when heated to a red heat and allowed to cool slowly. 
The process may be repeated many times without apparently changing the elastic pro- 
perties of the material. The yield-point, however, is found to alter in position as the 
annealings proceed. In a particular case f a mild steel bar, which in an ordinary test 
would give an extension of 25 per cent, upon a ten-inch length, and a yield-point of 
about 18 tons per square inch, was stretched approximately \ inch, and annealed in 
the ordinary manner after each operation. Throughout the experiment the bar appeared 
to recover its elastic properties after each annealing, and finally broke with a total 
extension of approximately 100 per cent. The yield-point remained fairly constant, 
except at the end, when it experienced a rise. 

Copper treated in the same manner has been drawn out by the author to consider- 
ably more than double its length in this way without causing fracture. Remarkable 
advances in our knowledge of annealing have been recently obtained by Mum,| acting 
upon a suggestion of Professor Ewing. 

Muir has shown that comparatively low temperatures, such as boiling water, will 
restore a strained bar to its elastic condition. The yield-point, however, alters during 
the process, and is always higher than in the original condition. 

After a few applications of stress, followed by heating in boiling water, or even water 
at 50° C, the bar fractures, with a total extension not very different from a bar stressed 
to breaking without special treatment. The annealing at low temperatures, therefore, 
appears to be less complete than that at a high temperature. 

In order to discover what effect a temperature of 100° C. would exert on a bar over- 
strained l>y a torque, the steel bar which had been used for experiments on the recovery 
of elasticity with time (see Section VI., Table IV.) was selected, and after being boiled for 
fifteen minutes was overstrained, giving results (col. X., Table XIV.) practically identical 
with those of col. I., Table IV., for the first part of the curve. As in practice it is 
troublesome to get exactly the same calibration value for each setting of the instrument, 
this latter (stripped of the reading microscope and wire holder) remained on the bar 
during the heating, and the labour of comparing readings whose unit values differed bv 

* Art. "Elasticity," Enc. Brit., Part 21. 

t (Joker, "Note on the Endurance of Steel Bars subjected to Repetitions of Tensional Stress." Proc. Inst. O.E., 1899. 

X "The Recovery of Iron from Overstrain." By James Muir. Phil. Trans., 1899. 



292 



DR E. G. COKER ON 



a small amount was thereby avoided. Each stress operation causing overstrain was 
succeeded by a heating in water at 100° C. for fifteen minutes, and in all the bar 
was stressed eight times. The readings obtained are given in columns X.-XVII. 
in Table XIV., and are plotted in the ordinary manner, fig. 29, the curves being 
spaced 100 units apart for convenience. As might be expected, the curves show a 
general agreement with those obtained by Mum, having regard to the fact that the 
stress is non-uniform. 

Table XIV. 



Column X. 


Column XI. 


Column XII. 


Column XIII. 


Torque in 
inch lbs. 


Keadin 


?■ A 


Torque in 
inch lbs. 


Reading 


A 


Torque in 
inch lbs. 


Reading 


. A 


Torque in 
inch lbs. 


Readin 


g- A 








385 








390 








389 








386 


75 


385 


385 


75 


390 


390 


75 


389 


387 


75 


386 


389 


150 


770 


388 


150 


780 


389 


150 


776 


389 


150 


775 


389 


225 


L15S 


387 


225 


1169 


389 


225 


1165 


389 


225 


1164 


388 


300 


1545 


389 


300 


1558 


388 


300 


1554 


387 


300 


1552 


389 


350 


1934 


392 


375 


1946 


391 


375 


1941 


389 


375 


1941 


389 


450 


2320 


389 


450 


2337 


390 


450 


2330 


388 


450 


2330 


392 


525 


2715 


395 


525 


2727 


388 


525 


2718 


389 


525 


2722 


388 


600 


3110 


400 


600 


3115 


392 


600 


3107 


389 


600 


3110 


389 


675 


3510 


404 


675 


3507 


390 


675 


3496 


386 


675 


3499 


394 


750 


3914 


426 


750 


3897 


394 


750 


3882 


391 


750 


3893 


402 


825 


4340 


463 


825 


4291 


410 


825 


4273 


398 


825 


4295 


402 


900 


4803 




900 


4701 


617 


900 


4671 


419 


900 


4697 


414 


930 


Went off scale 


975 


5318 




975 


5090 




975 


5111 














260 






303 






475 








990 


5578 




1025 


5393 




1050 


5586 










1015 


Went off scale 


1050 


Went off scale 


1080 


Went off scale 



APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS. 



293 



Table XIV. — continued. 



Column XIV. 


Column XV. 




Col 


umn XVI. 




Column XVII 


. A 


Torque in 
inch lbs. 


Reading. A 


Torque in 
inch lbs. 


Readiu, 


;• a 


Torque in 
inch lbs. 


Reading 


. A 


Torque in 
inch lbs. 


Reading 








386 








387 








387 








388 


75 


386 


387 


75 


387 


387 


75 


387 


387 


75 


388 


389 


150 


773 


384 


150 


774 


386 


150 


773 


387 


150 


777 


391 


225 


1157 


386 


225 


1160 


387 


225 


1159 


385 


225 


1168 


389 


300 


1543 


388 


300 


1547 


386 


300 


1544 


386 


300 


1557 


389 


375 


1931 


387 


375 


1933 


387 


375 


1930 


387 


375 


1946 


389 


450 


2318 


388 


450 


2320 


388 


450 


2317 


387 


450 


2335 


390 


525 


2706 


386 


525 


2708 


391 


525 


2704 


389 


525 


2725 


393 


600 


3092 


389 


600 


3099 


397 


600 


3093 


389 


600 


3118 


395 


675 


3481 


388 


675 


3496 


395 


675 


3482 


392 


675 


3513 


3!) 6 


750 


3869 


392 


750 


3891 


402 


750 


3874 


394 


750 


3909 


401 


825 


4261 


392 


825 


4293 


412 


825 


4268 


398 


825 


4310 


409 


900 


4653 


403 


900 


4705 


425 


900 


4666 


410 


900 


4719 


410 


975 


5056 


430 


975 


5130 


445 


975 


5076 


437 


975 


5129 


411 


1050 


5486 


197 


1050 


5575 


522 


1050 


5513 




1050 


5540 


458 


1080 


5683 




1125 


6097 




1105 


Went off scale 


1125 


5998 




1110 


Went off scale 


1155 


Went off scale 








1200 


Went off scale 



In conclusion the author desires to express his thanks to Prof. Bovey, Dean of 
the Faculty of Applied Science, M'Gill University, who placed the resources of the 
Testing Laboratory of the Civil Engineering Department at his disposal, and also to 
Mr Withycombe, Mechanica] Superintendent, who gave much help in the preparation 
of the apparatus 



Trans. Roy. Soc. Ellin. Vol. XL. 

Mr E. G. Coker on an "Apparatus for measuring Strain and applying Stress."— Plate I. 




Instrument for measuring angular distortion upon the specimen. 




Apparatus for applying the combined stresses of Bending and Torsion, 



Lb / y 




Trans. Roy. Soc. Edin. 



Vol. XL. 



Ph 



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Vol. XL. 



Dr. COKER: APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS.- Plate 




5 ->. p v 



■>■>, r 



■ 



oy. 



Soc. Edin. 



Dr. COKER: APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS.-Plate IV. 



Vol. XL. 







|,y. Soc. Edin. 



Vol. XL. 



Dr. COKER; APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS.-Plate Y 











/iS?^^ ^~ 



| - ;■-■-.!_ : .. 






Soc. E din. 



Vol. XL. 



Dr. COKER: APPARATUS FOR MEASURING STRAIN AND APPLYING STRESS.-Plate VI. 





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( 295 ) 



XV. — On the Anatomy of a Collection of Slugs from N.W. Borneo; with a List of 
the Species recorded from that Region. By Walter E. Collinge, Lecturer on 
Zoology and Comparative Anatomy in the University of Birmingham. Com- 
municated by Professor W. C. M'Intosh. (With Three Plates.) 

(Read 3rd June 1901.) 
CONTENTS. 



I. Introduction, 

II. The Bornean Slug-fauna, 

III. The Genus Damayantia, Issel, 

1. D. dilecta, Issel, 

2. I), carinata, n. sp., . 

IV. The Genus Wiegmannia, n. gen., 

1. W. dubius, Wgm., . 

2. W. gigas, n. sp., 

3. W. ponsonbyi, n. sp., 

4. W. borneensis, n. sp., 

5. W. sp., .... 
V. The Genus Collingea, Simr., . 

1. ft smithi, Cllge. and Godw.-Aust., 
VI. The Genus Isselentia, n. gen., 

1. I. plicata, n. sp., 

2. /. globosa, u. sp., 



page 
295 
296 
297 
298 
298 
299 
300 
300 
302 
302 
303 
303 
304 
305 
305 
307 



PAGE 

VII. The Genus Veronicella, Blainv., . . 307 

1. V. shelf 'or diana, n. sp., . . . 307 

2. V. exima, n. sp., .... 308 

VIII. The Genus Onchidium, Buchan. (em. Plate), 308 

1. (), ponsonbyi, n. sp., . . . 308 

IX. Summary and Conclusion, . . . 308 

X. List op Species op Slugs recorded prom 

Borneo, 309 

XL Bibliography, 310 

XII. Reference Letters, 310 

XIII. Description of Plates, .... 311 



I. Introduction. 

In the early part of 1900 I received from J. H. Ponsonby, Esq., a small collection 
of land molluscs from N.W. Borneo, with a request that I would investigate and report 
upon the same. This collection, the property of the Sarawak Museum, proved, on 
examination, to contain examples of two new genera ( Wiegmannia and Isselentia) of 
great interest. In the case of the former genus there were only two specimens, each 
belonging to a different species ; and as more material was very desirable, Mr Ponsonby 
very kindly invited the authorities of the Museum to send over, if possible, a further 
collection. This, in due course, arrived, but contained duplicates of Isselentia only, the 
remaining specimens being all new species, excepting one, which proved to be the 
Damayantia dilecta of Issel, which. I believe, has not previously been found since 
described in 1874. 

As there seems no immediate likelihood of obtaining further material, and so very 
little is known of the slugs of this region, the results of the examination of the 



VOL. XL. PART II. (NO. 15). 



2 X 



296 MR WALTER E. COLLINGE ON THE 

collection are now set forth, together with a list of the species of slugs which have 
been recorded from Borneo. 

I need scarcely say how deeply indebted I am to the great kindness of Mr Pon- 
sonby, and to the generous spirit shown by Mr R. Shelford and the authorities of the 
Sarawak Museum. My thanks are also tendered to Mr Edgar A. Smith, of the British 
Museum, for the many facilities he has given me for examining specimens in the 
collections under his charge. Finally, I wish to express my thanks to the Council of the 
Birmingham Natural History and Philosophical Society for defraying the expenses 
connected with the drawing of the accompanying figures. 

II. The Bornean Slug-fauna. 

It seems surprising that the Slug-fauna of Borneo has hitherto received so little 
attention. An island known to possess so rich a molluscan fauna, so far as the shelled 
forms are concerned, could not fail, one would think, to exhibit a wealth and variety of 
slug-like species. It does not, however, of necessity follow that the one always 
accompanies the other, at least so far as our present knowledge goes ; but this possibly 
may be due to the fact that very little serious collecting has been undertaken for those 
forms in which the shell is either absent or inconspicuous. As a case in point, I may 
instance the Indian and Chinese faunas. In the former region a very rich fauna of 
land-molluscs had been described long before any number of slugs were known. Up to 
the present time upwards of forty species are known, and I have collections in my 
possession, awaiting investigation, in which there are at least another eight or nine new 
species. An equally rich fauna of land-molluscs is found in China, but up to the 
present only about a dozen species of slugs are known from that region. 

One would presuppose, from the natural conditions of this island, that very many 
slug-like genera would be preesnt, and more careful investigation in Sarawak and the 
remainder of the island will, I am inclined to think, reveal a series of such of unusual 
interest. 

Issel (6), in 1874, in his well-known work, recorded six species, viz. : — 



Veronicella liasselti, v. Marts. 
Veronicella bleekeri, Kerfst. 
Veronicella wallarei, Issel. 



Parmarion becarii, Issel. 
Parmarion clorice, Issel. 
Damayantia dilecta, Issel. 



It is open to question if the two species placed in the genus Parmarion are rightly 
assigned. Cockerell (l) has placed the P. becarii in the genus lbycus, Heynemann, 
with the P. dories as a variety. From Issel's figures (6, T. iv. figs. 7-11), I am 
inclined to think that they both belong to the genus Wiegmannia. Nothing, however, 
being known of the internal structure of these forms, it is exceedingly difficult to say, 
with any certainty, what they are. Possibly the genus Parmarion, sens, str., does 
not occur in Borneo ; certainly nothing yet has been described from this region which 



ANATOMY OF A COLLECTION OF SLUGS FROM N.W. BOPvNEO. 297 

agrees with the genus as known from Java. If this view should ultimately prove to be 
correct, then the Bornean slug-fauna would show a closer agreement with that of the 
Philippines, rather than with that of Java. 

Damayantia is another genus peculiar to Borneo. Hitherto it has been known 
only from Issel's description ; it is now for the first time re-described, with some account 
of the anatomy and an emended description of D. dilecta, Issel. In the form of the 
mantle this genus undoubtedly shows affinities with the genera Philippinella, Mlldff. 
(8), and Parmunculus, Cllge. (2). 

In 1895 (3), in conjunction with Lieut.-Col. H. H. Godwin- Austen, I described a 
new species of Damayantia from Borneo, and two new species of Microparmarion, 
Simr. All three, however, were geuerically wrongly assigned. For the latter two Simroth 
(13) has constituted a new genus, Collingea, and in this the former must now be placed. 
In the same year Schepmann (10) described two new species — Parmarion goedhuisi 
and Microparmarion litteratus. Unfortunately no particulars of their internal structure 
were given, so that it is difficult to say if they are generically rightly named. 

Wiegmann (14), in 1898, described two further species — Parmarion macidosus 
and P. ? dubius. This latter I have in the present paper included in the new genus 
Wiegmannia. The former is perhaps the only species which approaches in its structure 
the true Parmarions, though it may possibly prove to be more nearly related to 
Wiegmannia. 

The remaining species all belong to the genus Veronicella, excepting one, the 
Oncidium nigrum of Plate (9). 



III. The Genus Damayantia, Issel. 

This genus was founded by Issel in 1874 (6) upon three specimens which he named 
D. dilecta. Accompanying the description, three excellent figures of the external 
features are given, but no account of the internal structure ; and as there is only one 
specimen in the present collection, I am, as yet, unable to supply this very desirable 
information. A new species, D. carinata, is now described, and I am able to give some 
details of its internal structure. 

Issel's original description # is incomplete, and in some points incorrect ; while some 
of the characters set forth are undoubtedly due to the contraction produced by the alcohol. 
His three specimens measured respectively 24, 17 '5, and 10 "5 millim. in length. The 
specimen I have examined was 28 millim. long. All the D. carinata were about 25 
millim. f 

* For comparison Issel's description is here reprinted. " Mollusco terrestre privo di conchiglia e di limacella 
Mantello convertito in sacco viscerale e collocato alia parte anteriore del corpo. Apertura respiratoria situata a destra 
del mantello ed vm po' all' imianzi. Orifizio genitale posto al lato destro del corpo. Testa munita di 4 tentacoli. Muso 
claviforme. Bocca sprovvista (?) di mandibola. Codo fornita di poro muccoso." 

t For a very careful translation of those parts of Issel's work relating to the Slugs of Borneo, I am indebted to my 
colleague, Professor C. BfevENOT. 



298 MR WALTER E. COLLINGE ON THE 

Damayantia, Issel (em. Cllge.). 

Damayantia, Issel: Moll. Bom., 1874, p. 389. 

Animal limaciform, long and tapering posteriorly, dorsum sharply keeled and 
definitely marked off from the posterior portion of the body ; anteriorly the dorsum is 
marked with two lateral grooves. Mantle, which completely covers the shell, exhibits 
a well-defined right and left keel, the right one overlapping the left posteriorly. 
Tentacles four. Visceral mass situated anteriorly, and lying more to the right side 
than the left. Rugse somewhat rhomboidal in shape, absent in the region of the mantle. 
Peripodial groove well defined. An obliquely placed, oval caudal mucous pore present. 
Generative orifice on the right side, slightly below and behind the right lower tentacle. 
Respiratory orifice on the right side of the mantle. Foot-fringe well marked. Foot-sole 
not divisible into median and lateral planes. Shell very small, almost entirely 
membranaceous. Receptaculum seminis sessile. Dart with solid calcareous head, at 
the base of which is a small opening. 

Damayantia is undoubtedly related to the genus Philippinella of Mollendorff (8). 

1. Damayantia dilecta, Issel. 

Damayantia dilecta, Issel : Moll. Born., 1874, p. 390, T. iv. figs. 4-6. 

PI. I. figs. 1-3. 

Animal yellowish-brown. Mantle completely covers the shell, minutely spotted 
with black. Keels well developed on the postero-lateral portions of the visceral mass 
and overlap one another posteriorly on the median line. The dorsum is sharply keeled. 
Ruga? small anteriorly, postero-laterally large and somewhat rhomboidal, absent on 
mantle. Caudal mucous pore large and overlapped by the extremity of the tail. 
Peripodial groove well defined. Foot-fringe yellowish in the anterior region, brownish 
posteriorly ; lineoles faint and set very closely. Foot-sole white, narrow, divided into 
median and lateral planes. 

Length (in alcohol) 28 millim. 

Hob. — Mt. Penrissen, 2800-3500 feet, 1 specimen. 

Issel (6, p. 28) mentions the presence of two longitudinal and medial furrows on the 
top part of the head, and at the sides two polygonous tubercles. In the specimen 
examined these features were not discernible. 

2. Damayantia carinata, n. sp. 
PL I. figs. 4, 5 ; PL II. figs. 22, 23. 

Animal greyish-brown, postero-laterally a faint dark band runs from the posterior 
end of the visceral mass to the tail ; lateral grooves well defined. Mantle completely 



ANATOMY OF A COLLECTION OF SLUGS FROM N.W. BORNEO. 299 

covers the shell ; posteriorly the two keels meet on the visceral mass, the right 
overlapping the left one. Posteriorly the body is sharply keeled, the keel being broken 
at irregular intervals, giving it a jagged or toothed appearance. Kugse small and 
indistinct, excepting on the postero-lateral portion, where they stand out conspicuously. 
Caudal mucous pore small. Peripodial groove distinct. Foot-fringe same colour as 
body with very faint, closely set, sepia-coloured lineoles. Foot-sole almost white, 
narrow. 

Length (in alcohol) 2 5 '5 millim. 

Shell membranaceous, thin, almost transparent, slight indication of apical whorl ; 
stria? faint ; ventrally there is a thin calcareous portion toward the apex. 

Maj. diam. G'8 ; min. diam. 5*5 millim., about. 

Hab. — Kuching, Mt. Penrissen, and Mt. Santubong, N.W. Borneo. 

Generative Organs. — (PL II. figs. 22, 23.) 

The male organ opens into the vestibule as a narrow tube, just beyond which it 
becomes enlarged and forms an ovoid sac, giving place again to a short tube-like portion 
which distally again becomes sac-like. At the distal end there is a short diverticulum. 
The retractor muscle is inserted on the right side at the distal end, almost opposite 
to which the short vas deferens connects the prostatic canal with the penis. The 
receptaculum seminis is a simple, pear-shaped, sessile sac, covered in life by the bend of 
the large dart-gland. There is a well-developed vagina ; the free oviduct is extremely 
short. The common duct is richly folded. The dart-gland is very large and has a 
sharp S-shaped bend at about the middle of its length ; distally there is a short 
retractor muscle. The dart (PI. II. fig. 23) is a hollow tube with a solid calcareous 
head ; at the base of the head is a small lateral opening. 

IV. The Genus Wiegmannia, n. gen. 

As already pointed out, Wiegmann in 1898 described a slug-like mollusc from 
Borneo, to which he gave the name Parmarion ? dubius. In the present collection there 
are four specimens which must be classed in the same genus as P. ? dubius. From the 
external characters and the internal structure, it is clear that they cannot be placed in 
the genus Parmarion, Fisch., or Microparmarion, Simr. I therefore propose a new 
genus for their reception, and have much pleasure in associating with it the name of 
Herrn Fritz Wiegmann of Jena, whose anatomical studies have so largely added to 
our knowledge of the mollusca of the Malayan Archipelago. 

In connection with Wiegmann's work (14), I may perhaps be permitted to point 
out that the Parmarion Jlavescens of Keferstein is not a Parmarion at all, but a 
true Urocyclus (7); further, that the Parmarion extranea, Fer., undoubtedly belongs 
to the genus Girasia, sens, str., agreeing, as it does, with the Indian forms, although 
it is extremely doubtful if the species figured by Semper is the extranea of Ferussac 
(cf. Godwin-Austen, 4, pp. 217-218). Semper imagined that the structure of 



300 MR WALTER E. COLLINGE ON THE 

Urocyclus Jlavescens, Kerfst., agreed pretty well with that of Parmarion papillaris, 
Himib., and Girasia extranea, Fer. : but I am not of this opinion (cf. Semper, Reis. 
Arch. Philip., p. 11). The literature relating to the Asiatic and Malayan slugs and 
slug-like molluscs abounds in similar inaccuracies. The two forms (Urocyclus Jlavescens, 
Kerfst., and Parmarion pupillaris, Humb.) are widely separated from one another, 
externally, anatomically, and geographically. 

WlEGMANNIA, II. gen. 

Animal Parmarion-like. Anteriorly the dorsum is marked with two lateral 
grooves, which, commencing from the sides of the head, converge towards the median 
line, and then pass to the right and left respectively. There is also a conspicuous row 
of rugse passing between these two lateral grooves in the mid dorsal line. Posteriorly 
the dorsum is keeled. The mantle shows faint traces of a keel, and has a thin shell 
border more or less covering the borders of the shell. Visceral mass large and lying 
upon a depression of the dorsum. Generative orifice immediately behind and below 
the right lower tentacle. Tail truncate, with large slit-like mucous pore which extends 
to the foot-sole. Dart-gland and sac large ; dart with solid, calcareous tip. Penis has a 
small diverticulum. Receptaculum seminis sessile. 

Shell a thin membranaceous sac, covering the posterior border of the visceral 
mass. 

1. Wiegmannia dubius, Wgm. 

Parmarion ? dubius, Wgm. : Abhandl. d. Senck. naturf. Gesell., 1898, Bd. ii. p. 105, T. xxi. figs. 27-40; 
T. xxii. figs. 1-6. 

For purposes of comparison, I have reproduced Wiegmann's figures of the externa] 
portion of the head and parts of the generative organs (PI. II. figs. 24-26), from which, 
1 think, it will at once be evident that this species belongs to the same genus as the 
following specimens. 

One point to be noted is that Wiegmann failed to find in either of his specimens 
any dart. He writes (14, p. 298): " Wahrend namlich die weibliche Anhangs- 
driise bei der Species von Java, ebenso wie bei P. pujrillo.ris nach Semper, nut einem 
Kalkigen Pfeile von sehr charakteristischen Form versehen ist, fehlt dieser ganzlich 
den beiden vorliegenden Tieren von Borneo, bei welchen die Pfeildrlise in einen durch- 
bohrten fleischigen Papille endigt." Judging from the figure of this fleshy papilla 
(14, Taf. xxi. fig. 40, and reproduced here on PL II. fig. 26), it has all the characters 
of a fundus, showing a dart in course of formation. 

2. Wiegmannia gigas, n. sp. 
PI. I. figs. 6-8; PL II. figs. 27, 28. 
Animal greyish-brown, with few blackish blotches on the sides of the body 
posteriorly. Head and tentacles dark blue, lateral grooves prominent, median line 



ANATOMY OF A COLLECTION OF SLUGS FROM N.W. BORNEO. 301 

of ruo-ge well marked. Mantle finely spotted with black ; posteriorly does not cover 
the visceral mass ; has a thin shell-border and faint trace of a keel. Extremity of 
foot truncate. Posterior portion of dorsum bluntly keeled. Rugae ill defined, 
fairly large laterally. Sulci blackish. Caudal mucous pore a longitudinal vertical 
slit extending to the foot-sole. Peripodial groove distinct. Foot-fringe same colour 
as the body with faint black lineoles. Foot-sole yellowish-brown, with two faint 
chocolate-coloured bands between median and lateral planes ; lateral planes marked 
by transverse lines, median plane papillated. 

Length (in alcohol) 50 millim., foot-sole 10 millim. Shell dark amber-coloured, 
membranaceous, faint trace of apical whorl. 

Hab. — Kuching, N.W. Borneo. 

This fine species is the largest I have seen of the genus. The visceral mass is 
considerably larger than in either of the two following species, and the keel on the 
mantle is only very feebly developed. 

Generative Organs. — (PI. II. figs. 27, 28.) 

The vestibule is a large, spacious cavity, into which the penis opens on the 
right side. This latter organ is very characteristic of the genus, differing in its. 
length, peculiar form, and the presence of a diverticulum, from the same organ in 
Parmarion and Microparmarion. In the present species it is folded upon itself at 
a distance of about one-third from its proximal end ; then forming a loop-like 
portion it enters the distal third ; at the distal end of the loop-like portion, a short 
retractor muscle is inserted, and at the commencement of the distal third there is 
a short diverticulum. I looked carefully for any trace of calcareous granules here, 
but did not succeed in finding any. Gradually tapering to a fine tube, the penis 
now passes imperceptibly into the long vas deferens, which joins the prostatic 
portion of the common duct on its left side (PI. II. fig. 27). The receptaculum 
seminis is a large, pear-shaped, sessile sac, and has, in this species, a short retractor 
muscle attached to its free end (PI. II. fig. 27). The vagina is a short tubular 
cavity with the small opening of the receptaculum seminis on the right side — when 
looked at from the anterior end — and the larger opening of the free-oviduct on 
the left. This latter organ is rather more than three times the length of the 
vagina ; it is coiled upon itself, making a single turn, and then passes into the 
larger, richly convoluted oviducal portion of the common duct, which is also folded 
upon itself toward the anterior end. A similar condition obtains in all the three 
new species here described. The albumen gland is large, as is also the flattened, 
elongated hermaphrodite gland, which latter has a comparatively short and slightly con- 
voluted duct. The dart-gland is a large and conspicuous organ, lying on the left ventral 
side. It has the usual fold at about its middle, and a short retractor muscle at its 
distal end (PI. II. fig. 27). The dart is smaller than in either of the two following- 
species ; it measures 3*7 millim. in length, is slightly curved, and the body, externally, 
is not differentiated from the head, which is a solid calcareous tip. 



302 MR WALTER E. COLLINGE ON THE 

3. Wiegmannia ponsonbyi, n. sp. 
PI. I. figs. 9, 10 ; PL II. figs. 29, 30. 

Animal yellowish-brown, with few, almost black, blotches and spots. Head 
almost black ; lateral grooves and median line of rugae well marked. Mantle same 
colour as body, comes upon all sides of the visceral mass, and has a thin shell- 
border and fairly well-developed keel. Extremity of foot truncate. Posterior 
portion of dorsum bluntly keeled. Rugae faintly marked. Sulci blackish. Caudal 
mucous pore a longitudinal vertical slit extending to the foot-sole. Peripodial groove 
prominent. Foot-fringe same colour as the body ; lineoles black. Foot-sole almost 
black anteriorly, posteriorly same colour as the body ; divided into median and 
lateral planes. 

Length (in alcohol) 42 millim. 

Shell same as in W. gigas, only smaller and reddish-brown in colour. 

Hab. — Kuching, N.W. Borneo. 

Generative Organs. — (PI. II. figs. 29, 30.) 

The external form of the penis differs considerably from that of W. gigas or 
W. dubius, Wgm. ; it is much shorter and is not folded to anything like the same 
extent. From the vestibule as far as the diverticulum it is uniform in circumference ; 
opposite the diverticulum there is a small retractor muscle inserted. The distal 
portion of the penis gradually tapers, giving place to the vas deferens (PL II. fig. 
29). The receptaculum seminis is small, somewhat pear-shaped, and opens into the 
right side of the vagina. This latter organ is much longer than in the preceding 
species and exhibits a slight constriction just beyond its anterior third. The free- 
oviduct, on the other hand, is very short. The dart-gland is similar to that in W. 
gigas, only larger and not so uniform in shape, exhibiting a series of constrictions 
and dilatations in the anterior (PL II. fig. 29, d.s.). Structurally the dart 
is the same as that in W. gigas, but in this species the one present was much 
more fragile, and a little over twice the length of that found in the preceding 
species (PL II. fig. 30). 

4. Wiegmannia borneensis, n. sp. 

PL I. figs. 11, 12 ; PL II. figs. 31, 32. 

Animal brownish-yellow with faint blackish mottling on the fore part of the 
head and dorsum, lateral grooves and median line of rugae well marked. Mantle 
same colour as body with dark mottling ; comes upon all sides of the visceral mass ; 
has a thin shell-border ; keel more conspicuous posteriorly. Extremity of foot 
truncate. Posterior portion of dorsum keeled. Rugae large. Sulci sepia coloured. 
Caudal mucous pore a vertical slit extending to the foot-sole. Peripodial groove 



ANATOMY OF A COLLECTION OF SLUGS FROM N.W. BORNEO. 303 

distinct. Foot-fringe same colour as the body, with faintly coloured lineoles. Foot- 
sole brownish-yellow with median and lateral planes. 

Length (in alcohol) 49 millim. 

Shell a thin membranaceous sac, reddish-brown in colour, with very faint lines of 
growth ; apical portion distinct. 

Hab. — Kuching, N.W. Borneo. 

Generative Organs. — (PL II. figs. 31, 32.) 

The generative organs agree more closely with those of W. gigas than with 
those of W. ponsonbyi. The vestibule is sac-like, and the vagina long, as in W. 
ponsonbyi. The penis is folded upon itself at a distance of about one-third from 
its proximal end ; this and the middle portion form a fairly wide tube, which now 
gradually tapers until it passes into the vas deferens. At the point where the 
retractor muscle is inserted (PL II. fig. 31, div.) there is a small diverticulum. The 
receptaculum seminis is a somewhat ovoid-sbaped sac opening on the right side of 
the vagina. The free-oviduct is proportionally not so long as in W. gigas, but 
longer than in W. ponsonbyi. The dart-gland is very similar in shape to that in 
W. gigas, but the dart-sac contained a dart more like that described for W. ponsonbyi, 
differing, however, in possessing a more perfectly developed head, with a longer, solid, 
calcareous tip (PL II. fig. 32). 

5. Wiegmannia, sp. 

A small, bluish-grey form, measuring 14 millim. in length (in alcohol) ; may possibly 
be a further new species. The mantle border is finely spotted, and posteriorly it rises 
around the visceral mass, and has a well-developed keel encircling it. I await further 
material before naming the specimen. 

Hab.—Mt. Penrissen, 2800-3500 feet. 

V. The Genus Collingea, Simr. 

Collingea, Simr. : Zool. Jahrb. (Abth. f. Syst.), 1898, Bd. ii. p. 168. 

In 1895 (3), I described, in conjunction with Lieut. -Col. H. H. Godwin-Austen, a 
slug-like mollusc from the Poeh Mountains, Sarawak, to which the name Damayantia 
smithi was given. At that time I had not seen Issel's description (6) and figures of 
D. dilecta; but Lieut. -Col. Godwin- Austen was of opinion that the specimens from the 
Poeh Mountains belonged to Issel's genus. Having recently seen a specimen of D. 
dilecta and compared it with Issel's description and figures, I have no hesitation in at 
once removing the specimen named D. smithi from that genus. 

Through the kindness of Mr Edgar A. Smith, I have had the opportunity of 
re-examining this very interesting mollusc, and am now able to give an emended descrip- 
tion of it and some further particulars respecting its internal structure. 

Unfortunately, a very serious error was made at the time it was originally described. 

VOL. XL. PART II. (NO. 15). 2 Y 



304 MK WALTER E. COLLINGE ON THE 

Mr Edgar A. Smith sent me three specimens. One of these Godwin- Austen figured 
(3, pi. xi. figs. 1-6), which undoubtedly belongs to the genus Collingea, Simr. One of 
the remaining two I dissected, and described and figured the generative organs (cf. 3, pi. 
xi. figs. 9-11) ; but, unfortunately, this was very distinct from the one which Godwin- 
Austen figured, and on re-examining it I find that it and its fellow belong to the genus 
Isselentia here described (p. 305). 

The specimen of Collingea smithi had been opened, and I have made a careful 
examination of the generative organs, and figures of these are now given for the first 
time (PI. II. figs. 34-36). The peculiar handle-like extension of the penis (the Henkel 
of Simroth) at once characterises this species as belonging to the genus Collingea. 

Godwin-Austen has given (5, pp. 55-57) what he terms an amended description of 
both the animal and anatomy of what was originally termed Damayantia smithi. The 
description of the animal, of course, applies to Collingea smithi, whilst the anatomical 
account applies, in so far as it is correct, to Isselentia globosa (p. 305). It is doubtful 
if Godwin- Austen refers to a true Damayantia, especially as he compares these two 
molluscs with D. dilecta. Issel's figures (6, T. iv. figs. 4-6) show how different the 
genus is from C. smithi or /. globosa. 

This author, on p. 58, writes : "I illustrate the anatomy of Microparmarion with my 
original drawings (those in the P. Z. S., 1895, being copies of them*)." The figures in 
the P. Z. S. paper, which are credited to me, were made by me from the dissections. 

1. Collingea smithi, Cllge. and Godw.-Aust. 

PI. II. figs. 33-36. 

Damayantia smithi, Cllge. and Godw.-Aust. : Proc. Zool. Soc, 1895, p. 242, pi. xi. figs. l-i. 
Damayantia smithi, Godwin- Austen : Moll, of India, 1898, vol. ii. p. 55, pi. lxxiii. figs. 1-7 d. 

Animal : body yellowish, with dark blue or bluish-brown mottling on the sides in 
the posterior region. t. Mantle yellowish-grey with irregular dark blue or black 
mottling ; has a thin shell-border and distinct lateral keel. Extremity of foot truncate. 
Posterior portion of dorsum sharply keeled. Rugse large. Caudal mucous pore large, 
but does not extend to the foot-sole. Peripodial groove well marked. Foot-fringe 
yellowish-brown with faintly marked lineoles. Foot-sole darker than the foot-fringe 
and divided into median and lateral planes. 

Length (in alcohol) 28 millim. ; breadth of foot-sole 4 '5 millim. 

Shell oval, membranaceous, thin, and shiny ; apical whorl distinct (PL II. fig. 33). 

Hab. — Poeh Mountain (3500 feet), Sarawak (A. H. Everett). 

Type in collection of British Museum. 

Generative Organs. — (PI. II. figs. 34-36.) 

The vagina is a wide, sac-like cavity, on the left side of which the receptaculuni 

* The italics are mine. — W. E. C. 

+ Originally described as a "very dark blue or black streak runs along the side of the foot posteriorly, crossing it 
diagonally downwards to the mucous pore." The figure is wrong in showing this. 



ANATOMY OF A COLLECTION OF SLUGS FEOM N.W. BORNEO. 305 

semiuis opens. This is an irregular-shaped sac with a short duct. The penis is a 
thick, muscular-walled tube, narrow at its proximal end, but increasing in size as it 
nears the distal end, where it makes a sharp bend to the right, this distal extremity 
forming a sac-like extension (PI. II. fig. 34, 35). On the left-hand side is a loop- 
like extension — the Henkel of Simroth. The vas deferens leaves the distal extremity 
of the penis on its ventral side (PI. II. fig. 36, v.d.). The retractor muscle also is inserted 
on the ventral side, at the point where the penis makes a sharp bend to the right, 
(PI. II. fig. 36, r.m.). The dart-gland (PI. II. fig. 34. d.gl.) is a large, muscular organ ; 
distally it presents a swollen appearance which occupies about one-half; the proximal 
half is tube-like. 

Compared with the three known species of Collingea, viz., C struhelli, Simr., 
C. pollonerai, Cllge. and Godw.-Aust., and C. simrothi, Cllge. and Godw.-Aust., this 
species approaches most nearly to C. simrothi. It differs considerably from C. strubelli 
(12) in the form of the penis and dart-gland, and in the same manner from C. pollonerai. 

VT. The Genus Isselentia, n. gen. 

Animal slug-like. The mantle anteriorly forms two wing-like appendages lying on 
each side of the visceral mass, inner borders plicated or folded, comes up around the 
posterior and lateral borders of the visceral mass ; shell-borders thin. Dorsum 
posteriorly keeled. Generative orifice behind right lower tentacle. Small caudal mucous 
pore. Foot-sole divided into median and lateral planes. Viscera elevated into the dorsal 
hump, the body-cavity not extending beyond it into the tail, which is solid. 

Generative system : penis with or without diverticulum. Sessile receptaculum 
seminis. Dart calcareous, with small laterally placed aperture. 

1. Isselentia plicata, n. sp. 
PI. II. figs. 13-156 ; PI. III. figs. 37-49. 

Animal yellowish with dark blue dorsum posteriorly, head bluish. Mantle reddish- 
yellow, with small blackish spots and blotches ; shell-border thin. Posterior portion of 
dorsum exhibits a wavy keel of a deep yellow colour. Rugse more or less ovoid. 
Caudal mucous pore small and partly hidden by the extremity of the dorsum. Peripodial 
groove very prominent. Foot-fringe yellow, with fine, very closely set lineoles. Foot- 
sole yellowish, divided into median and lateral planes. 

Length (in alcohol) 26 millim. 

Shell amber-coloured ; a thin membranaceous sac ; apical whorl distinct. 

Hob. — Mt. Penrissen and Mt. Santubong. 

Generative Organs.— (PI. III. figs. 37-49.) 

The penis is of considerable length ; it has a somewhat globose proximal portion, 
followed by a narrower portion, again expanding and narrowing, and terminating by a 



306 MR WALTER E. OOLLINGE ON THE 

sharp bend, gives place to a somewhat conical head. The whole of the distal end is 
-covered with connective tissue, so that at first sight it has the appearance shown in 
fig. 37 (PI. III.). When, however, this is dissected away, the S -shaped bend is seen, the 
tube becoming gradually larger as it nears the point where the retractor muscle is 
inserted (PI. III. fig. 38). The external wall exhibits a series of ring-like constrictions ; 
one of these immediately beyond the retractor muscle is much deeper and sharply divides 
the "head" into two parts, viz., that already described and the conical portion beyond, 
which has similar constrictions. This gradually tapers off into the vas deferens (PI. III. 
fig. 37). The vagina is a long, wide tube, having an opening on its dorsal wall for the 
small, twisted receptaculum seminis, and a larger opening at its posterior end for the 
small globular free-oviduct. The first portion of the common duct is sharply coiled upon 
itself. The dart-gland (PI. III. fig. 37, d.gl.) when viewed externally exhibits a globose 
distal portion, to which a small retractor muscle is attached, a middle tube-like portion, 
forming the bend, and a dart-sac, the proximal portion. Three specimens were examined. 
In the first the dart was immature, and had the peculiar bent form shown in fig. 40 
(PI. III.). In the second specimen this was in much the same condition. In the third, 
however, a well-formed dart was present, measuring 4 millim. in length. The dart is 
situated at the posterior end of the proximal sac-like portion. Externally the dart is 
covered by a calcareous sheath, which has a small, lateralty placed, oval-shaped aperture. 
The head is not differentiated from the body, which is almost straight and about the 
same thickness throughout (PI. III. figs. 39-42). 

Under a high power of the microscope, the calcareous layer is seen to consist of an 
outer structureless layer, and an inner one which, when looked at longitudinally, has the 
appearance of short dark and light bands (PI. III. fig. 41). This inner layer is more 
conspicuous in the region of the head than elsewhere. The basal end or annulus 
(PL III. fig. 43) fits into a groove ; and so far as I could make out the structure, which 
proved very difficult, the internal cavity of the dart is continuous with that of the 
expanded distal portion of the dart-gland (PL III. fig. 44). 

The dart-gland consists of a thin external sheath of connective tissue, within which is 
a longitudinal muscular layer, and then a layer of circular muscle fibres with a few 
radial fibres intermixed, some of these latter extending as far as, and into, the longitudinal 
layer. The central cavity is bounded by an epithelial lining (PL III. figs. 45 and 47). 
Longitudinal and transverse sections were made of both the proximal and distal 
portions. The former has a glandular lining, and when looked at in surface view, the 
wall has the appearance of being studded with a series of bluntly pointed papillae 
(PL III. fig. 49). In longitudinal section these are seen to consist of an outer epithelial 
layer of cuboid cells, and an inner layer of almost circular cells (PL III. figs. 46 and 48). 
In the distal portion the epithelial lining consists of columnar cells, and the cavity 
contains a larger series of exceedingly minute particles (calcareous ?) imbedded in a 
jelly-like matrix. Sections cut by a freezing microtome were stained in an aqueous 
solution of magenta, but the matrix remained unstained. Others were treated with 



ANATOMY OF A COLLECTION OF SLUGS FROM N.W. BORNEO. 307 

5 and 10 per cent, solutions of hydrochloric acid, but no effect was obtained. Strong 
hydrochloric acid caused the matrix to coagulate. 



2. Isselentia glohosa, n. sp. 
PL III. fig. 50. 

Animal smaller but not at all unlike I. plicata ; the ground colour, however, is 
lighter, and the posterior portions of the dorsum considerably lighter. The plications 
of the mantle lobes are only slightly developed. 

Hob. — Poeh Mountain (3500 feet), Sarawak (A. H. Everett). 

Type in collection of British Museum. Two specimens. 

When recently examining these two specimens, I felt inclined to refer them to 
/. plicata, but an examination of the generative organs shows that they exhibit some 
important differences. 

Generative Organs. — (PL III. fig. 50.) 

The vestibule is small. The penis consists of a sac-like portion, above which it 
becomes suddenly constricted and then dilates into a bulbous head. From the distal 
portion of the penis, above the vas deferens, is a short diverticulum, partially covered 
by the strong retractor muscle (PL III. fig. 50). From the side of the bulbous head of the 
penis the vas deferens passes off as a thick tube, narrowing gradually as it approaches the 
prostatic portion of the common duct. The receptaculum seminis is somewhat ovoid 
and sessile, and opens into the vagina ; to the right of this is the opening of the free- 
oviduct. The first portion of this organ is thrown into a series of constrictions. The 
oviduct is a wide tube and densely folded, the prostatic and oviducal portions 
terminating in a bulbous head lying immediately in front of the globular albumen gland. 
The hermaphrodite gland is almost circular and flattened, showing a slight fold or 
indentation in the centre. The dart-gland is a large, thick, muscular-walled tube, making 
a sharp S-shaped bend distally. Just below this is the dart-sac, which contains a 
calcareous dart similar in shape to that in /. plicata (PL III. fig. 39), but whether or 
not it is perforated I cannot say, as the head had been broken away. 



VII. The Genus Veronicella, Blainv. 
1. Veronicella shelf ordiana, n. sp. 
PL I. figs. 16, 17. 

Animal dark-brown dorsally, with dense yellow spotting and median dorsal 
yellowish-brown stripe. Hyponotum and foot-sole light-brown. 

Length (in alcohol) 20 millim. ; foot-sole 2*5 millim. broad; hyponotum 4 millim. 
broad. Female generative orifice on the right side, 3 millim. from the foot-sole, 11-5 



308 MR WALTER E. COLLINGE ON THE 

niilliin. from the right lower tentacle, and 8 '5 millim. from the posterior end of the 
body. 

Hab. — Kuching, N.W. Borneo. 

I have pleasure in associating with this handsome species the name of Mr 
Shelford of the Sarawak Museum. 

2. Veronicella exima, n. sp. 
PI. I. figs. 18, 19. 

Animal yellowish-brown dorsally, densely and minutely speckled with black, 
leaving a clear unicolourous margin and broad medio-dorsal line. Hyponotum 
yellowish-brown ; foot-sole brown. 

Length (in alcohol) 22 '5 millim.; foot-sole 2 millim. broad; hyponotum 3 '5 
millim. broad. Female generative orifice on the right side, 3 millim. from the foot- 
sole, 12*5 millim. from the right lower tentacle, and 12 millim. from the posterior 
end of the body. 

Hab. — Kuching, N.W. Borneo. 

VIII. The Genus Onchidium, Buchan. (em. Plate). 

1. Onchidium ponsonbyi, n. sp. 
PI. I. figs. 20, 21. 

Animal dirty green dorsally with large, irregularly distributed black spots. 
Hyponotum dark greenish-blue ; foot-sole dirty yellow. 

Length (in alcohol) 30 millim.; hyponotum 10 millim. ; foot-sole 8 millim. 

Hab.— Mt. Penrissen (2800-3500 feet). 

It gives me much pleasure to associate with this very fine species the name of 
Mr Ponsonby. 

IX. Summary and Conclusion. 

From an examination of the foregoing specimens it is, as yet, difficult to 
generalise as to their affinities or relationships with allied genera, for our knowledge 
of their structure and specific variation is too fragmentary. Further, it is of little 
use comparing the form and structure of the generative organs of such genera 
as Wiegmannia and Isselentia with Parmarion, Microparmarion, etc., for our 
knowledge of the structure of these latter genera is not much more complete. I 
sincerely hope, however, that with the invaluable aid of Mr Shelford and other 
naturalists, I shall be able, before long, to treat of the general anatomy of many of 
the Bornean slugs in much greater detail. The present communication must be 
regarded more in the light of a preliminary notice of species, which, as further 
material is obtained, will receive more exhaustive treatment. 



ANATOMY OF A COLLECTION OF SLUGS FROM N.W. BORNEO. 309 



X. List of Species of Slugs recorded from Borneo. 

Damayantia, Is9el : Ann. Mus. Civ. Genova, 1874, vi. p. 26. 

1. D. dilecta, Issel : Ibid. p. 27, T. iv. figs. 4-6. 

2. D. carinata, Cllge. : Ante, p. 298. 

Wiegmannia, Cllge. : Ante, p. 299. 

3. W. dubius, Wgm. : Abhandl. d. Senckenb. naturf. GeselL, 1898, p. 305, T. xxi. figs. 27-40, T. xxii. 

fig. 1-6. 

4. W. gigas, Cllge. : Ante, p. 300. 

5. W. ponsonbyi, Cllge. : Ante, p. 302. 

6. W. borneensis, Cllge. : Ante, p. 302. 

7. W., sp. : Ante, p. 303. 

Collingea, Simr. : ZooZ. Jahrb. (Abth. f. Syst.), 1898, Bd. ii. p. 168. 

8. C. pollonerai, Cllge. and Godw.-Aust. : Proc. Zool. Soc, 1895, p. 244, pis. xii., xiii., figs. 

13-25. 

9. C. simrotlti, Cllge. and Godw.-Aust. : Ibid. p. 246, pis. xii., xiii., figs. 26-35. 

10. C. smithi, Cllge. and Godw.-Aust. : Ibid. p. 242. 

Ibycus, Heyn. : Mai, Blatt., 1862, p. 142, pi. 1, fig. 3. 

11. I. beccarii, Issel: Ann. Mus. Civ. Genova, 1874, vi. p. 23, T. iv. figs. 9-11. 

12. /. dorice, Issel : Ibid. p. 25, T. iv. figs. 7, 8. 

Parmarion, P. Fischer : Actes. Soc. Linn. Bordeaux, 1855. 

13. P. maculosus, Wgm. : Abhandl. d. Senckenb. naturf. Gesell, 1898, p. 299, T. xxi. figs. 8-26. 

14. P. goedhuisi, Schepm. : Notes Jr. Leyden Mus., 1895, vol. xvii. p. 146, pi. 2, figs. l«-lc. 

Microparmarion, Simr. : Zool. Ergebnisse, 1893, Bd. iii. p. 104. 

15. M. Utteratus, Schepm. : Notes Jr. Leyden Mus., 1895, vol. xvii. p. 148, pi. 2, figs. 2a-2c. 

Isselentia, Cllge. : Ante, p. 305. 

16. I. plicata, Cllge. : Ante, p. 305. 

17. /. globosa, Cllge. : Ante, p. 307. 

Veronicella, Blainv. : Jouni. de Physique, 1817, p. 440, pi. vi. figs. 1, 2. 

18. V. bleekeri, Kerfst. : Zeit. f. iciss. Zool, 1865, Bd. xv. p. 125, T. ix. figs. 1-7. 

19. V. hasselti, v. Marts. : Die Landschnecken Preuss. Exped. nach Ust-Asien, 1867, p. 176, T. v. 

figs. 2, 4. 

20. V. Jlava, Heyn. : Jahrb. Deutsch. Malad. Gessel., 1885, Bd. xii. 

21. V. idee, Semp. : Reisen im Arch. Philip., 1885, Heft. vii. p. 321. 

22. V. borneensis, Simr. : Abhandl. d. Senckenb. naturf. Gesell., 1897, Bd. xxiv. p. 142, T. xiv. figs. 

8, 15, 16, 17. 

23. V. wallacei, Issel : Ann. Mus. Civ. Genova, 1874, vi. p. 22, T. iv. figs. 1-3. 

24. V. shelfordiana, Cllge. : Ante, p. 307. 

25. V. exima, Cllge. : Ante, p. 308. 

Onchidium, Buchan. (em. Plate): Trans. Linn. Soc, 1800, vol. v. p. 132. 

26. 0. nigrum, Plate: Zool. Jahrb. {Abth. f. Morph.), 1893, Bd. 7, p. 188, T. 8, fig. 31a; T. 10, 

fig. 53; T. 11, fig. 75. 

27. 0. ponsonbyi, Cllge.: Ante, v. 308. 



310 



MR WALTER E. COLLINGE ON THE 



XL Bibliography. 

1. Cockereli., T. D. A., "A Check-List of the Slugs," Conchologist, 1893, vol. ii. pp. 168-176 and 

185-232. 

2. Collinge, Walter E., " On the Anatomy and Systematic Position of the Genus Philippinella, 

Mlldff.," Semper's Reisen im Arch. d. Philip., 1899, Bd. viii. pp. 54-60, T. viii. 

3. Collinge, Walter E., and Godwin-Austen, H. H., " On the Structure and Affinities of some new 

Species of Molluscs from Borneo," Proc. Zool. Soc, 1895, pp. 241-250, pis. xi.-xiv. 

4. Godwin- Austen, H. H., Land and Freshwater Mollusca of India, vol. i. pts. i.-vi., 1882-1888. 

5. Godwin- Austen, H. H., Land and Freshwater Mollusca of India, vol. ii. pts. vii.-ix., 1897-1899. 

6. Issel, A., "Molluschi Borneensi," Annali d. Museo Civico Genova, 1874, vol. vi. pp. 366-486, 

T. iv.-vii. 

7. Keferstein, W., " Ueber Parmarion (Urocyclus) flavescens, n. sp.," Malak. Bldtt., 1866, Bd. 

xiii. pp. 72-76, T. ii. 

8. Mollendorff, 0. F. vou, "'Diagnoses specierum novarum ex insulis Philippines," Nadir, d. 

Deutsch. Malak. Gesell., 1894, pp. 81-121. 

9. Plate, L. H., "Studien fiber opisthopneumone Lungenschnecken. II. Die Oncidiiden," Zool. 

Jahrb. (Abth. f. Morph.), 1893, Bd. vii. pp. 93-234, Taf. 7-12. 

10. Schepmann, M. M., "The Mollusca of the Dutch Scientific Borneo Expedition, with description of 

the new species," Notes from the Leyden Mus., 1895, vol. xvii. pp. 145-162, pis. 2-4. 

11. Semper, C, Reisen im Archipel der Philippinen, 1870, Th. II. Bd. iii. " Landmollusken." 

12. Simroth, Heinrich, " Ueber einige Parmarion- Arten," Zool. Ergebnisse einer Reise in Niederlandisch 

Ost-Indien, 1893, Bd. iii. pp. 100-111, T. vii., viii. 

13. Simroth, Heinrich, " Ueber die Gattungen Parmacochlea, Parmarion und Microparmarion" 

Zool. Jahrb. (AUh.f. Syst.J, 1898, Bd. ii. pp. 151-172, T. 15. 

14. Wiegmann, F., " Landmollusken (Stylommatophoren) Zootomischer Teil," Abhandl. d. Sencicenb. 

naturf. Gesell., 1898, pp. 289-557, Taf. xxi.-xxxi. 



XII. Reference Letters. 



alb.gl. Albumen gland. 
ap. Aperture of dart. 
c.d. Cavity of dart. 
c.d.gl. Cavity of dart-gland. 
c.e. Columnar epithelium. 
c.t. Connective tissue. 
cm. Circular muscle fibres. 

d. Dart. 
d.gl. Dart-gland. 
d.s. Dart sac. 

div. Diverticulum of penis. 
ep. Epithelium. 
f.ov. Free-oviduct. 
gl. Gland cells. 
H. Henkel. 
h.d. Hermaphrodite duct. 



h.gl. Hermaphrodite gland. 

i.c.l. Inner calcareous layer. 

l.m. Longitudinal muscle fibres. 

l.p. Lateral plane of foot-sole. 

m.p. Median plane of foot-sole. 

o.c.l. Outer calcareous layer. 

ov. Oviduct. 

p. Penis. 

pr. Prostate. 

r.m. Retractor muscle. 

r.m.f. Radial muscle fibres. 

r.s. Receptaculum seminis. 

v. Vestibule. 

v.d. Vas deferens. 

vg. Vagina. 




ANATOMY OF A COLLECTION OF SLUGS FROM N.W. BORNEO. 311 



XIII. Description of Plates. 



Plate I. 



Fig. 1. Damayantia dilecta, Issel. Lateral view, x 2. 

Fig. 2. „ „ „ Dorsal view, x 2. 

Fig. 3. „ ,, ,, Dorsal view of shell, x 1|. 

Fig. 4. Damayantia carinata, n. sp. Lateral view, x 2. 

Fig. 5. ,, „ Dorsal view, x 2. 

Fig. 6. Wiegmannia gigas, n.sp. Lateral view, x 1. 

Fig. 7. „ „ Dorsal view of the head, showing lateral grooves and median row of 

rugae, x 2. 
Fig. 8. ,, „ Foot-sole showing median and lateral planes, x 3. 

Fig. 9. Wiegmannia ponsonbyi, n.sp. Lateral view, x 1. 

Fig. 10. „ „ Dorsal view of the head, x 2. 

Fig. 11. Wiegmannia borneensis, n. sp. Lateral view, x 1. 

Fig. 12. „ „ Dorsal view of the head, x 2. 

Fig. 13. Isselentia plicata, n. sp. View from the right side, x 2. 

Fig. 14. „ „ View from the left side, x 2. 

Fig. 15. „ „ Dorsal view, x 2. 

Figs. 15a, b. ,, „ Dorsal and ventral view of shell, x 1. 

Fig. 16. Veronicella shelfordiana, n. sp., as seen from above, x 2. 

Fig. 17. ,, „ as seen from below, x 2. 

Fig. 18. Veronicella exima, n. sp., as seen from above, x 2. 

Kg. 19. „ „ as seen from below, x 2. 

Fig. 20. Onchidium ponsonbyi, n. sp., as seen from above, x 1. 

Fig. 21. ,, „ as seen from below, x 1. 

Plate II. 



;i 



ig. 22. Damayantia carinata, n. sp. Generative organs, 
ig. 23. „ „ Dart, x 16. 

> Wiegmannia dubius, Wgm. Parts of the terminal ducts of the generative organs (after Wiegmann). 
g. 25. J 

g. 26. ,, „ Dart (after Wiegmann). 

ig. 27. Wiegmannia gigas, n. sp. Generative organs. 

g- 28. „ „ Dart, x 16. 

g. 29. Wiegmannia ponsonbyi, n. sp. Generative organs. 

ig. 30. „ „ Dart, x 16. 

ig. 31. Wiegmannia borneensis, n. sp. Generative organs. 

ig. 32. „ „ Dart, x 18. 

g. 33. Collingea smithi, Cllge. and Godw.-Aust. Shell, x 2*5. 

g- 34. „ „ ,, Generativeiorgans. 

•B« 35. „ „ „ Dorsal view of penis, etc, 

g. 36. „ „ „ Ventral view of penis, etc. 

VOL. XL PART II. (NO. 15). 2 Z 



312 MR WALTER E. COLLINGE ON A COLLECTION OF SLUGS. 



Plate III. 

Fig. 37. Isselentia plicata, n. sp. Generative organs. 

Fig. 38. „ ,, Distal end of penis, enlarged. 

Fig. 39. „ „ Dart, x 15. 

Fig. 40. „ „ Immature dart. 

Fig. 41. ,, ,, Head of dart, highly magnified. 

Fig. 42. „ „ Portion of immature dart, showing bends in calcareous sheath. 

Fig. 43. „ „ Diagrammatic view of fundus. 

Fig. 44. „ ,, Distal end of dart-gland showing cavity. 

Fig. 45. ,, „ Diagrammatic view of a transverse section through the distal portion of 

the dart-gland. 

Fig. 46. „ „ Longitudinal section through the proximal portion of the dart-gland. 

Fig. 47. „ „ Transverse section through the distal portion of the dart-gland. 

Fig. 48. „ „ Epithelial and gland cells from the proximal portion of the dart-gland. 

Fig. 49. ,, „ Surface view of the internal wall of the dart-gland, proximal portion. 

Fig. 50. Isselentia globosa, n. sp. Generative organs. 










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XVI. — The True Shape, Relations, and Structure of the Alimentary Viscera of 
the Porpoise (Phoccena communis), as displayed by the Formal Method. (With 
Lantern Demonstration of their Microscopic Structure.) By David Hepburn, 
M.D., F.RS.E., Lecturer on Regional Anatomy, and David Waterston, M.A., 
M.D., F.R.S.E., Demonstrator of Anatomy, University of Edinburgh. (With 
Three Plates.) 

(Read July 15, 1901.) 



TABLE OF CONTENTS. 



Introductory .... 
Method of Preparation . 
External Appearances . 
Cavity of Abdomen 
Peritoneal Folds and Reflections 
Absence of Foramen of Winslow 
Stomach— First Compartment 
„ Second „ 

„ Third „ 

' „ Fourth ,, 



Pylorus 



PAGE 

313 
313 
314 
315 
315 
316 
317 
319 
321 
322 
324 



Duodenum 324 

Bile Duct 324 

Pancreatic Duct 324 

Intestine 325 

Pancreas 326 

Liver 326 

Spleen 319, 327 

Conclusions 327 

Literature . . 328 

Explanation of Figures 329 



Introductory. — Among the toothed whales (Odontoceti) the porpoise is the best- 
known representative of those members of the genus Delphinus or true dolphins which 
present a rounded muzzle as distinguished from a snout, and consequently it has 
already frequently been subjected to anatomical examination of a more or less detailed 
character. As in the case of all the Cetacea, however, the rapidity with which decom- 
position affects the various tissues and organs has hitherto proved a barrier to a 
prolonged and systematic examination of them, while, even under the most favourable 
conditions, the increasing putridity of the carcase has seriously militated against the 
recording of accurate observations. 

Accordingly, when a porpoise, which had been captured in some fishing nets twenty- 
four hours previously, came into our possession last December, we took immediate steps 
for its perfect preservation, so that its dissection might be conducted at leisure under 
conditions of comfort as well as accuracy, and its various tissues "fixed" for reliable 
examination by the microscope. 

Method of Preparation. — We therefore first recorded the measurements and 
external appearances of the animal, and then, having placed it upon its back in such a 
way as to remove all pressure from its dorsal fin, we opened a comparatively small vessel 
on its ventral aspect between the anus and the tail. Into thin vessel — a small vein 

TRANS. ROY. SOC. EDIN., VOL. XL. PART II. (NO. 16). 3 a 



314 



DRS HEPBURN AND WATERSTON ON THE 



immediately under cover of the blubber — we tied a fine canula having a lumen which 
would admit the stilette of a dissector's blowpipe. Through this vessel we injected, by- 
means of a gravitation pressure of about four feet, about two gallons of an arsenical 
preservative to which 10 per cent, of formaldehyde had been added. The fluid took 
several hours to run into the animal, the body meanwhile becoming firm and rigid, but 
not in any way distended or deformed. The success of this method of preservation has 
been apparent at every stage of the dissection. After seven months, the carcase is 
still absolutely devoid of unpleasant odour, and no trace of decomposition is visible 
anywhere. The blood has been everywhere coagulated in the vessels, which are thus 
filled with a natural solid injection mass. The viscera have been fixed so as to retain 
their natural shapes and relationships. The tissues are all in perfect condition for 
undergoing further treatment in preparation for the microscope, with the exception of a 
slight desquamation of a few superficial cells from the mucous membrane of the 
alimentary canal. In our examination of this animal, therefore, we are in a position 
to present observations, made under conditions which we believe to be unique, which 
give results of a thoroughly reliable kind, besides being in many respects entirely novel 
and which no doubt account for differences between our results and those of former 
observers. 

External Appearances. — The animal, which was a male, presented the character- 
istic features of its genus as regards its rounded muzzle, its teeth, the comparatively 
high position of its fore limbs upon its sides, the colour of its body and appendages, the 
tuberculated border of its dorsal fin, etc. The following measurements were recorded 
before the preservative fluid was injected : — 

Length from tip of muzzle to centre of tail, 

,, from muzzle to vent, 

„ from vent to centre of tail, 

,, of oral cleft, 

„ from muzzle to anterior edge of root of flipper 

„ from muzzle to dorsal fin, 

,, of flipper, 
Width of tail, 
Girth of tail at root, 

Distance between genito-urinary cleft and vent, 
Length of base of dorsal fin, 
Height of dorsal fin, 
Distance from external angle of eye to external 

auditory meatus, ....... 2 „ 051 „ 

There were nowhere any traces of hair, and no evidence of an external ear, while 
the external auditory meatus would not admit the stem of a wax vesta. As the adult 
porpoise is usually from four to five feet long, although it may reach a length of six feet, 
the present specimen may be regarded as slightly under its full growth. 

In the present communication we desire to confine our attention to that part of the 
alimentary system contained within the cavity of the abdomen. 



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SHAPE AND STRUCTURE OF ALIMENTARY VISCERA OF PORPOISE. 315 

Cavity of Abdomen. — On opening the abdominal cavity by removing the ventral 
wall, it was found that the general shape of the cavity was oval, the anterior end was 
more obtuse than the posterior, and the greatest transverse diameter was opposite the 
lower or hinder border of the liver. The upper (anterior) part contained the liver and 
greater part of the stomach, while the posterior part was filled by the convoluted mass 
of the intestine. 

The border of the liver extended across the cavity from a point opposite the eighth 
right costo-chondral junction to a corresponding point on the left side, in an almost 
transverse direction ; and near the mesial plane of the body there was a triangular notch 
which was occupied by a small portion of the wall of one of the chambers of the 
stomach, while another small part of the stomach wall projected from below the border 
of the left lobe, but only for three-quarters of an inch. The coils of intestine of were 
practically the same calibre throughout, and were suspended from the dorsal wall by a 
single mesial mesentery. There was no sign of a vermiform appendix, or csecum, and 
no part of the tube showed to the naked eye any of the appearances characteristic of 
the large, as distinguished from the small, intestine. 

The abdominal cavity measured 36*5 cms. in its long axis, and 19 "5 cms. in its 
maximum transverse diameter, and at the posterior end it narrowed suddenly, and 
opened by a definite constricted orifice into an elongated tubular chamber, the 
representative of a pelvic cavity (PL I. figs. 1 and 2). The aperture was formed by a 
projecting margin of peritoneal membrane, over which the vasa deferentia turned in 
their course to the urethra. The diameters of this orifice were 25 cms. in the sag- 
gital axis, by 1*5 cm. in the transverse, and the depth of the chamber was 7 cms. 
This tubular peritoneal recess passed between the pelvic bones ventrally, and the 
vertebral column dorsally, and formed the lining membrane of a chamber, which, from 
its position, contents, and boundaries, we regard as the representative of a pelvic cavity. 
The projecting margin on either side corresponded to the brim of a true pelvis. The 
relations of the viscera associated with the peritoneum confirm the analogy, as the 
urinary bladder lay between the peritoneum of its ventral wall and the pelvic bones 
and interpubic ligament, while the rectum descended in relation to the dorsal wall, 
being supported by a mesentery at its upper or anterior part, but gradually losing its 
peritoneal investment to end in the anal canal. Hitherto, this arrangement of the 
peritoneum does not seem to have been recognised as a pelvic cavity, although Turner * 
in a description of the posterior end of the abdominal cavity of Risso's Dolphin 
{Grampus griseus), refers to the peritoneum as forming " four csecal pouches," of 
which the dorso-mesial one apparently corresponds to the pelvic cavity which we 
have described. 

Peritoneal Folds and Reflections. — The falciform ligament of the liver and the 
Ligamentum teres were both distinct, and were almost mesial in position. The former 
disappeared into a vertical slit, 5 cms. in length, in the ventral surface of the liver. 

* Sir Wm. Turner, Jour, of Anat. and Phys. t vol. xxvi. p. 264. 



316 DRS HEPBURN AND WATERSTON ON THE 

A peritoneal fold of the nature of a great omentum was represented by a short fold, 
not more than 6 cms. in length, depending from the curvature of the stomach, where 
it appeared from under cover of the liver, but did not contain any quantity of fatty 
tissue. The coils of intestine were suspended from the posterior or dorsal abdominal 
wall by a single mesial fold or mesentery, in which near the root there were large masses 
of lymphatic tissue, which diminished in size towards the caudal end. The lower end 
of the intestine passed into the pelvic chamber mesially, and was suspended by a 
continuation of the mesentery. 

The absence of any intestinal coil corresponding in position to the colon rendered the 
arrangement of the peritoneum about the stomach and pancreas somewhat unusual. 

The great omentum, already described as depending from the stomach, was composed 
of four layers of peritoneum — two ventral and two dorsal. On tearing through the 
ventral layers, a lesser sac of peritoneum was opened, whose boundaries were as 
follows : — 

Ventrally, the wall of the stomach ; dorsally, pancreas ; on the left, the first 
chamber of the stomach ; and on the right side, the last part of the stomach and the 
duodenum. 

No aperture corresponding to a foramen of Winslow could be found, and the arrange- 
ment of the peritoneal membrane was more clearly brought out by examining it from 
behind, after removing the viscera en bloc. 

The lesser sac was then seen to be completely closed in by the peritoneum, which 
had the following attachments : — 

The anterior layers of the great omentum, attached to the greater curvature of 
chamber No. 2 of the stomach, were prolonged on the left side to the posterior 
surface of chamber No. 1, from which they were reflected off along an oblique line 
from the centre of its ventral border to the spleen. 

Above the spleen,the two layers separated to envelop the oesophagus. The two 
posterior or dorsal layers pass dorsally to the border of the pancreas, where they 
diverge, one passing on the anterior ventral surface, and the other to the inferior caudal 
surface of that viscus. 

On the right side, the layers passed on to the duodenum, and then backwards on to 
the posterior abdominal wall and pancreas, and thus on the right side the lesser sac 
became completely closed. 

The apex of the pancreas was in contact with the under surface of the liver. 

The absence of an aperture into the lesser sac * may be explained by reference to the 
relative positions of the stomach, liver, and pancreas. The pancreas, instead of lying 

* In a monograph entitled, " Recherches sur le deVeloppement de la cavite hepato-enterique de l'Axolotl et de 
l'arriere cavite" du peritoine chez les mammiferes (Lapin), par Albert Brachet, Archives de Biologie, tome XIII., 1893, 
pp. 559-618 (Plates XXIV. to XXVII.), the following passage occurs : — " La fermeture de cet hiatus" (de Winslow) 
" chez l'amphibien, provient de ce que le bord posterieur du m£so-lateral est tres peu etendu, et que dans son 
interieur ne penetre pas le foie. Ce bord, se continuant dans le mesoduod^num a son extremite inferieure, se soude 
peu a peu a lui, de bas en haut. L' union entre les deux, progressant dans ce sens, aniene Pocclusion de l'hiatus." 



SHAPE AND STRUCTURE OF ALIMENTARY VISCERA OF PORPOISE. 317 

behind the lesser sac, with its head in the concavity of the duodenum, was found be- 
tween the duodenum and the liver projecting to the left side, so as to be related to the 
first and second chambers of the stomach within the folds of the lesser omentum. The 
alteration in the peritoneal relations is best realised by supposing the pancreas to have 
moved to the right and forwards (ventrally), and then upwards (anteriorly) between 
the upper border of the duodenum and the liver, thereby separating the layers of the 
gastro-hepatic omentum, and pressing its posterior or dorsal layer into contact with the 
peritoneum covering the dorsal wall of the abdomen, until these two opposite walls of 
the lesser sac have fused together. That there has been an alteration of this kind is 
shown by the fact that the bile-duct has no free course, but from the under surface of 
the liver enters the head of the pancreas and remains in it, until it pierces the wall of 
the duodenum, and by the further fact that there is a reflection of peritoneum from the 
under surface of the liver to the back of the head of the pancreas, completely occluding 
any communication between the sac which lies on the dorsal aspect of the stomach and 
the general or great peritoneal cavity. Furthermore, that part of the liver bounded by 
the obliterated ductus venosus and the inferior vena cava (Lobulus spigelii), was 
situated on the dorsal aspect of the liver, and was entirely devoid of peritoneal covering. 
On the other hand, the Lobulus caudatus, situated on the dorsal aspect of the hilum of 
the liver, was associated with a blind digital process of peritoneum. 

Between the layers forming the ventral part of the omentum, there was a curious 
arrangement of lymphoid tissue. There wss a large number of bloodvessels in the 
peritoneal membrane, and these vessels passed through small nodules of lymphoid 
tissue, so that they produced the appearance of a bunch of grapes on a stalk, and the 
arrangement closely resembled the condition present in the human spleen when the 
vessels are isolated from the spleen tissue. A similar condition was not found in the 
other parts of the peritoneum. 

Stomach. — As is well known, the stomach of this animal has been the subject of 
much debate. Observers have agreed that it presented four compartments, but they 
have differed as to the homologies and the sequence of these chambers, and, therefore, 
their special interest in the present instance is due to the fact of their having been fixed 
in a normal position so that they show their natural shapes, and consequently their 
homologies can readily be understood. 

The different chambers composing the complex stomach had the following positions 
and relations : — 1. The first and second chambers lay side by side, the first being 
situated on the dorsal aspect of the other compartments, and somewhat to the right side 
of the second compartment. The first compartment received the oesophagus at its 
anterior end, and formed a somewhat conical bag, not unlike a cardiac ventricle, measur- 
ing about five and a half inches (14 cms.) in the antero-posterior or long diameter, 
and three and a half inches (9 cms.) in the dorso-ventral direction. The axis of the 
chamber was a direct continuation of that of the oesophagus. It had two borders and 
two surfaces. The one border was dorsal in position, straight in character, and carried, 



318 DRS HEPBURN AND WATERSTON ON THE 

about its middle, a small spleen aiid an accessory mass of lymphoid tissue. The other 
border, ventral in position, was curved, and was in two parts. The anterior part was 
blended with the coats of the second chamber, while the posterior half was free, and 
united only by a peritoneal fold to the second chamber in the anterior half. 

The surfaces were left dorsal, and right ventral. The former was free and entirely 
invested by peritoneum. The latter was flat, and in its upper part was in contact with 
the left surface of the pancreas, which here projected into the angle between chambers 
1 and 2. This surface was crossed obliquely by the line of reflection of the 
peritoneum. The interior was filled with food consisting of fish which had been crushed 
and triturated so that the flesh was entirely removed from the bones, while the latter 
were, for the most part, disarticulated from each other. The food was moist, but not at 
all wet or pulpy, so that the treatment to which it had been subjected in this chamber 
might be called " dry mastication." The interior of this " kau-magen " presented 
appearances which quite corresponded with its apparent functions. Its walls were 
covered by a thick, white, almost porcellaneous lining, which was everywhere thrown into 
bold, prominent ruga?. On the ventral wall of the chamber, and immediately behind the 
oesophageal opening, the rugse were thrown into a cauliflower-like projection, and in the 
centre of this mass a careful examination revealed the outlet of the chamber. The inlet 
and outlet were thus remarkably close to each other, but, besides being situated at right 
angles to each other, the manner in which the outlet was concealed within a mass of 
prominent rugae made it quite impossible for food to enter indiscriminately from the 
oesophagus into the second, as well as the first, compartment. In the first instance, it 
was only possible for food to enter the first chamber. To the naked eye, the lining 
membrane was continuous with, and of the same nature as, the lining membrane of the 
oesophagus. 

Under the microscope (PI. II. fig. 3), the lining membrane was found to be situated 
upon a well-marked layer of loose areolar tissue in which numerous capillary blood- 
vessels ramified. Its vertical thickness measured almost 1 cm. The free surface 
was extensively but not deeply corrugated, while its deep surface was interrupted by 
numerous narrow clefts extending towards the free surface for varying distances, but 
usually not more than half-way. The whole arrangement was closely suggestive of 
the rete malpighi and stratified epithelial layers of skin, while the areolar tissue and 
vascular prolongations, which occupied the subjacent furrows or clefts, bore a close 
resemblance to the arrangement of the papillae of the true skin. In the deeper layers, 
the cells of this lining membrane presented rounded nuclei, which stained deeply. 
Nearer to the free surface the nuclei stained less distinctly, but their rounded character 
was well maintained. Comparatively close to the surface, the nuclei became markedly 
flattened, and, at the same time, the cell stratification became pronounced. At this 
level also, and onwards to the free surface, the tissue was distinctly paler because it 
absorbed less of the staining agent. At no part of the membrane was there any 
trace of any arrangement for secretion. 



SHAPE AND STRUCTURE OF ALIMENTARY VISCERA OF PORPOISE. 319 

There has been much discussion as to whether this compartment should be 
regarded as a part of the stomach, or merely a post-diaphragmatic diverticulum of 
the oesophagus. We have already shown that it carries the gastro-splenic omentum, 
and possesses the general peritoneal relations which one associates with the stomach, 
and there can be no doubt that it acts simply as a triturator of the food. Moreover, 
since the outlet is situated at right angles to the inlet, it is highly improbable that 
food could pass from the inlet to the outlet without first of all making its way through 
the triturator. Again, as the food which was found in the compartment was not 
digested, there appears no reason to suppose that any digesting, takes place in this 
chamber as the result of the regurgitation of gastric juice into it from the second 
compartment. 

In consideration of the nature of the teeth with which the porpoise is provided— 
viz., tearing teeth and not grinding teeth— it appears highly advantageous that the 
stomach should be so specialised as to supply the necessary grinding or triturating 
apparatus through the action of a chamber which is able to crumble food exactly as 
a piece of bread might be reduced to powder by the crushing action of the hand. 
We do not regard the similarity between its lining membrane and that of the 
oesophagus as of itself a sufficient reason for concluding that it is a diverticulum of 
the oesophagus, from the fact that in a one-chambered stomach the oesophageal 
lining membrane may be prolonged for some distance upon the interior of the stomach — 
e.g., in the pig; while from the general, but, more especially, the splenic, relations of 
this first compartment, we are of opinion that it must be regarded as an undoubted 
specialisation of the stomach, and not of the oesophagus. The peritoneal mesenteric 
or omental connection between this chamber and the spleen gives a strong argument 
for recognising the chamber as stomach, especially as the spleen always develops within 
tbe mesentery which attaches the primitive stomach, and not the oesophagus, to the 
dorsal wall of the abdominal cavity. That this association of the spleen with the first 
compartment of cetacean stomachs is not peculiar to the porpoise, has been shown 
by Sir Wm. Turner, who has recorded # a similar arrangement in the stomachs of 
Hyperoodon rostratus, Delphinus delphis, Delphinus (Lagenorhynchus) albirostris, 
Monodon monoceros, and Grampus griseus. We think that the term " kau-magen," 
or masticatory stomach, would fairly express its function and its morphology. 

The second compartment, which was situated on the ventral aspect of the first, 
and formed an acute angle with it, had very much the shape of the human stomach, 
and presented two surfaces, two borders, and two apertures, but the chief axis lay 
more in the long axis of the abdominal cavity than does that of the human stomach. 
The ventral surface, rounded and convex, was in contact with the liver and the anterior 
abdominal wall. The dorsal surface looked towards the lesser peritoneal sac, and was in 
contact with the pancreas and chamber 1. The greater curvature measured 16 cms., 
and had an omentum attached to it; the lesser border measured 12"5 cms. In contact 

* Turner, Jour, of Anat. and Phys., vol. xxiii. pp. 466-492, vol. xxvi. pp. 258-270. 



320 DRS HEPBURN AND WATERSTON ON THE 

with this border, from left to right, were the pancreas, a peritoneal fold, and the 
recurved tubular part of the stomach for a distance of 6 cms. The apertures were 
situated, not at the ends, but in the walls or curvature. When opened, it was 
empty, and its cavity was only slightly smaller than that of the first chamber. "With 
the exception of the external layer of muscle, the mucous and muscular coats were 
raised into thick prominent rugse, separated from each other by deep intervening 
furrows. Although these rugae were indented by mutual pressure, yet they resembled 
cerebral convolutions on a small scale. Their general disposition was in the long 
axis of the cavity, but, though running for the most part parallel to each other, they 
converged around the inlet and outlet of the chamber. 

As already indicated, the inlet was placed upon the dorsal aspect of the chamber, 
and was at right angles to the line of entrance of the oesophagus into the first com- 
partment. The appearances might be simulated by making a tight constriction round 
a one-chambered stomach close below its oesophageal orifice, and then applying the long 
contiguous sides of the two parts closely together. However, the sharp angle between 
the two compartments was occupied by the loose folds of the great omentum, so that 
neither of the chambers was prevented from distending, by its peritoneal relationships. 
Thread parasites adhered to the lining membrane, which was smooth and of a rusty 
brown colour. 

Under the microscope, the secreting mucous membrane was from 2 to 3 mms. thick 
(PL IT. fig. 4 (a)), and it closely invested the strong muscular ridges, which, as already 
indicated, resembled cerebral convolutions or large columnse carneae. It consisted 
essentially of tubular glands (PI. II. fig 4 (b)) supported upon a very distinct muscularis 
mucosas, which sent definite prolongations, accompanied by a fine fibrous stroma, among 
the closely arranged tubules. The intertubular tissue was plentifully provided with 
capillary vessels. 

The glands occupied the entire thickness of the mucous membrane, and each gland 
presented two parts, distinguishable from each other by structural differences. First, 
each gland, from its mouth inwards for a distance of '04 mm., consisted of a delicate 
basement membrane lined by short columnar cells, which surrounded a circular lumen 
— the duct of the gland — and stained after the manner characteristic of duct cells. The 
cells which had covered the free surface of the mucous membrane had been mostly 
desquamated, but so far as could be ascertained, they were similar to those lining the 
ducts just described. The gland proper constituted the remainder and second part of 
the secreting apparatus. Each tubule appeared to become branched as it passed inwards 
from the surface, but, judging from the fact that transverse sections of the tubules 
were not found in the deeper levels of the mucous membrane, the amount of tortuosity 
was not great. Each tubule (PI. II. fig. 4 (b)) presented magnificent examples of central 
and parietal cells. The central cells were large nucleated polyhedral cells, set closely 
together and bounding the irregular lumen of the tubule. Everywhere they stained very 
deeply. The parietal cells formed a continuous single layer of cells, globular in shape 



SHAPE AND STRUCTURE OF ALIMENTARY VISCERA OF PORPOISE. 321 

and set in intimate contact with the basement membrane, which sent prolongations 
inwards between them towards the central cells. As a result, each of the parietal cells 
occupied a recess or pocket exactly as if it lay in one compartment of a honeycomb. 
The parietal cells were not quite so large as the central cells, and from the fact that the 
former separated quite readily from the latter, one judged that there was no very definite 
uniting medium. The products of the activity of the parietal cells would find their 
way into the lumen of the tubule through fine interstices between the central cells, and 
these interstices were visible or concealed according to the direction of the section. 
Each parietal cell might be regarded as a unicellular secreting gland. They were filled 
with coarse eosinophile granules. It is important to note that these cells formed an 
unbroken layer, and that they were situated next to the blood supply, and that, therefore, 
they intervened between the central cells and their direct blood supply. In presenting 
a continuous layer of parietal cells, these tubular glands differ from those with which 
they correspond in such animals as the dog, the bat, and even in man, in all of which 
they only occur at intervals in the walls of the tubules. It is also of interest to note 
that these oxyntic cells are definitely restricted to one compartment of the stomach of 
the porpoise, whereas in the single-chambered stomachs of the other mammals above 
referred to, they are specially characteristic of the fundus, although not exclusively 
confined to that region. 

The intertubular stroma everywhere showed very well marked capillary vessels, and 
throughout the stroma, more especially towards the free side of the mucous membrane, 
numbers of lymph cells were scattered. 

From the ventral aspect of this compartment, and about one inch (2 "5 cms.) in front 
of its most dependent part, a small constricted passage, wide enough to transmit the 
handle of a rod 5 mms. in diameter, led into the third compartment (PI. III. fig. 10b). 
This passage was quite concealed among the thick muscular rugse of the second 
chamber, and its exact position would scarcely be suspected from an examination of 
the second chamber. Viewed from the third compartment, however, it presented the 
appearance of a small firmly constricted aperture opening backwards. We feel assured 
that this is nothing more than a mural passage from the second to the third chamber. 
Tt has been regarded by Jungklaus as a separate chamber, supplying in itself the 
third chamber, which has long been sought for in order to complete the analogy 
between the stomach of the porpoise and that of other cetacea. But the necessity 
for doing this disappears, since the method we have employed reveals the presence of 
a distinct globular third chamber, entirely separate from the second and fourth com- 
partments, and outside of the mural passage, which is required as an outlet from the 
second to the third compartments. The third compartment was situated somewhat 
behind and on the ventral aspect of the second, to which it was closely adherent by the 
surface next the inlet without the intervention of peritoneum ; but on its dorsal and 
ventral surfaces the peritoneum was prolonged from the second compartment without 
interruption, and, moreover, it had the great omentum attached to the hinder border of 

TRANS. ROY. SOC. EDIN., VOL. XL. PART II. (NO. 16). 3 b 



322 DRS HEPBURN AND WATERSTON ON THE 

its free surface. This globular chamber was marked off from the distal tubular part by 
a constriction visible externally, and well marked internally. The walls of this chamber 
were little more than one-sixteenth of an inch (less than 2 mms.) in thickness. The lining 
mucous membrane was pale, very slightly rugose, and at frequent intervals it presented 
pin-point depressions surrounded by slightly raised rings of the mucous membrane. This 
chamber was found empty, but it appeared capable of holding, without distension, 
material equal in bulk to the size of a small orange. While the inlet opened backwards 
to the second compartment, the outlet opened forwards into the fourth compartment. 
The adjacent margins of these two openings were about three-eighths of an inch (9 mms,) 
apart. The outlet was not so firmly constricted as the inlet, and could transmit the tip 
of a little finger without being unduly stretched. 

Examined microscopically (PI. II. fig. 5), the mucous membrane was found to rest 
upon a thick layer of muscularis mucosae, which everywhere sent prolongations into the 
intertubular intervals. As in the preceding compartment, the surface layer of epithelium 
had been desquamated, but otherwise the tissue was in a satisfactory condition. It formed 
a layer averaging about 5 mms. in thickness, and throughout it presented large numbers 
of tubular glands. At intervals in its deeper half spherical nodules of lymphoid tissue 
appeared, while all through the intertubular stroma, which was considerable in amount, 
large numbers of lymph corpuscles were visible. These were most numerous in the 
immediate vicinity of the lymph nodule. The tubular glands appeared to be fairly 
simple in their arrangement, and in all probability they do not always branch as 
they descend into the substance of the mucous membrane. When they do divide, it is 
probably not oftener than once. Towards their deeper ends they appear to follow a 
sinuous course, and they may there be somewhat convoluted. The end next the surface 
tends to be straighter and less wavy. A delicate basement membrane supported the 
cells which lined the glands. These cells were somewhat cubical in shape, and, while 
their nuclei were always quite distinct, yet those pertaining to the superficial part of the 
tubules stained much more deeply than those belonging to the deeper part of the gland. 
A transverse section of the deep end of a tube examined under a higher power (PI. II. 
fig. 6) revealed a small circular lumen surrounded by a close-fitting layer of nucleated 
cells. There was no trace of any arrangement corresponding to parietal cells. The 
tubules of this and of the succeeding compartment may very fairly be likened to the 
pyloric glands of other mammals, but instead of being scattered among oxyntic glands 
and only predominating near, or being exclusively found in the vicinity of the pylorus, 
they are restricted to the third and fourth compartments, and are not intermingled 
with oxyntic glands. 

Vessels of different sizes were readily visible in the submucous layer, but the pene- 
tration of capillaries into the intertubular stroma was not very great, as in the case of 
the second compartment. It would therefore appear as if the vascularity of this mucous 
membrane was not a prominent characteristic of its structure. 

The succeeding or fourth compartment was shaped like an inverted V (/\), of which 



SHAPE AND STRUCTURE OF ALIMENTARY VISCERA OF PORPOISE. 323 

the proximal limb was rather shorter than the distal one. A small amount of constriction 
was observed at the angle of the A, while at its termination it was bent slightly for- 
wards. It would be possible to describe this segment of the stomach as two chambers, 
but that seems to be uncalled for, in view of the fact that the microscopic characters of 
its mucous membrane did not, in any special manner, differ from those detailed for the 
third compartment. Indeed, there is reason to believe that this entire segment is, in 
reality, one chamber of nearly uniform cylindrical appearance, capable of being divided 
into a larger or smaller number of subdivisions by means of septa or circular con- 
strictions more or less pronounced. It is this chamber which is so frequently divided 
in the narwhal. They might very well correspond to the pyloric half of the human 
stomach subdivided by constrictions. The proximal limb of the A-shaped compartment 
was situated in front of the third chamber and in close apposition with the lesser 
curvature of the second, to which it was intimately connected by direct prolongations of 
the peritoneum upon their free surfaces. The great omentum was also continued into 
the angle formed by the limbs of the V. Like the preceding compartment, it was empty. 
From its inlet to the slight constriction at the angle of the V measured three and a half 
inches (9 cms.) in length by one and a half (38 mms.) in width. The general form of 
this segment of the chamber was an elongated oval. 

Its walls, as regards thickness, were similar to those of the preceding chamber. The 
mucous membrane was pale, showing only a faint amount of rugosity ; thereby indicating 
that it did not require to undergo much distension. At intervals pin-point depressions 
like those already noted in the preceding chamber were observed. At the point of the 
V — i.e., at the acute angle — there was a certain narrowing of the lumen which might be 
described as constriction, or might be referred to the mere acute bending. The micro- 
scopic features of the mucous membrane did not differ in any marked way from those 
already described in connection with the third compartment, but the tubules were 
probably rather shorter, and the mucous membrane slightly thinner. 

The distal limb of the inverted V extended to the pylorus. It virtually formed a 
cylindrical tube measuring about five inches (13 cms.) in length, and directed backwards 
and to the right. Within one inch (2 '5 cms.) of the pylorus it underwent a slight dilatation 
on its hinder aspect, forming an Antrum pylori. At the same time it turned forwards with 
considerable abruptness, to end at the pylorus. Along its anterior and somewhat concave 
aspect it afforded attachment for the gastro-hepatic omentum. Between the laminse of 
this omentum, masses of lymphatic gland were found towards its left end, and the head 
of the pancreas occupied a similar position in relation to the pylorus at the right end 

The mucous membrane was very slightly rugose, and presented numerous pin-hole 
depressions, each of which, as in the places already mentioned, was surrounded by a 
slightly raised ring of the mucous membrane. Microscopically the mucous membrane 
did not present any variation upon what has been stated in connection with the last two 
compartments (PI. III. figs. 7a and b). Apparently the pin-hole depressions may be 
associated with the nodules of lymphoid tissue which are everywhere embedded in the 



324 DRS HEPBURN AND WATERSTON ON THE 

mucous membrane of the second and subsequent compartments. Whether these nodules 
communicate directly with the lumen of the intestine we cannot say, but we have not 
found any trace of surface epithelium superficial to these nodules in any part of the 
alimentary canal, where they occur embedded in the mucous membrane. There is 
plentiful evidence that these nodules push their way entirely through the stratum of 
tubular and intertubular tissue of which the mucous membrane consists. If they are 
covered over by a layer of surface cells, as is generally supposed, there are certainly 
no glandular structures between them and the lumen of the canal. In their whole 
structure they present a remarkable similarity to the faucial tonsils of man, and they 
may serve a similar purpose. 

The Pylorus. — The pyloric orifice was a tightly constricted passage which, with 
some pressure, would admit a rod 5 mms. in diameter. It was situated in the middle 
of a projection somewhat like an exaggerated nipple. The actual orifice was found 
on the summit of this nipple, which was directed into the interior of the compartment 
backwards and to the right side. 

Every one of these constricted passages was placed as if with the definite object 
of making the onward progress of the contents as difficult as possible, and only 
attainable after the most complete circuit of the compartment. The length of this 
canal was rather more than half an inch (16 mms.). In its general arrangement and 
appearance it resembled the canal which formed the passage of communication from the 
second to the third compartments. Still no one has ever proposed that the pyloric 
passage should be adduced as a separate chamber, and so we regard Jungklaus' state- 
ment upon the third chamber as an error in homology. 

The Duodenum. — Beyond the pylorus, the intestine commenced with a marked 
dilatation, whose diameter at first resembled that of the adjoining part of the stomach. 
Very soon, however, it slightly increased in size, but after a course of two and a half 
inches (6'5 cms.), it suddenly dwindled and assumed the general characters of the 
remainder of the intestine. 

Immediately before this dilatation became reduced to the proportions of the ordinary 
bowel, it received the bile-duct which penetrated its dorsal surface. Further, the 
pancreas was closely applied to this portion of the canal, but the pancreatic duct formed 
a tributary of the bile-duct, and so did not show a separate opening through the wall. 
This disposition of the pancreatic ducts was not surprising, since the bile-duct passed 
through, and was therefore surrounded by the head of the pancreas. From this 
disposition of these important ducts we are justified in regarding this section of the 
canal as the duodenum, which therefore corresponds to what are called the first and 
second parts of the human duodenum. 

On being opened, the duodenum was seen to be lined by a mucous membrane con- 
siderably darker in colour than those which had lined the preceding compartments of the 
stomach. Whether this colour should be attributed to staining by bile we cannot say, 
as there was no gall-bladder, and therefore we saw no bile. It was thrown into promi- 



SHAPE AND STRUCTURE OF ALIMENTARY VISCERA OF PORPOISE. 325 

nent rugae, and presented a miniature copy of the interior of the second stomach 
chamber. Its capacity was about equal to that of the third compartment of the 
stomach. The opening of the bile-duct was situated on a papilla {Papilla voteri) on 
the dorsal wall of the duodenum, about half an inch (12 mms.) from the termination. 
This termination was not marked by any valvular constriction, but was merely indicated 
by a sudden reduction in calibre to the shape and proportions of the intestinal tube. 

From such a distinct and precise disposition of this portion of the canal there can be 
no reasonable doubt that, so far as this animal is concerned, the duodenum should not be 
regarded as a section of the intestine, but rather as a separate and special chamber 
within which the liquid or peptonised food, having left the stomach, is subjected to the 
action of the biliary and pancreatic secretions. It was a contention of the late Professor 
Goodsir that the duodenum of man ought to be considered as a separate segment of the 
bowel, on account of its attachments, structure, and functions. On these points, so far as 
the porpoise is concerned, this view is quite clearly supported. 

Microscopically, the mucous membrane was remarkable for its negative as well as for 
its positive characters. Villi were entirely wanting from its surface, and there were no 
trace of Brunner's glands. 

The rugae already mentioned formed longitudinal ridges of muscularis mucosae 
covered by the lining mucous membrane, which consisted of tubules similar to those 
found in the adjoining intestine. 

The surface epithelium was, for the most part, denuded, but on some remaining 
patches the cells were short and cubical. Each gland was comparatively straight, the 
duct being lined by short columnar epithelium, while the deeper part of the gland 
presented a considerable number of chalice cells. 

The intestine, which commenced at the end of the duodenum, extended to the anal 
aperture as a tube of uniform appearance and supported by a single mesentery. In 
calibre it appeared to be also fairly uniform, and although some parts were more firmly 
contracted than others, there was no outward evidence of division into large and small 
bowel. In its general appearance it resembled small bowel, and its least contracted 
parts were not larger than the diameter of an average digit. No diverticulum or 
appendix occurred anywhere. It measured rather more than fifty feet in length — i.e., 
nearly twelve times the length of the animal. 

When we consider that the length of the human intestine is only from four to five 
times as long as the individual, we are probably justified in associating the unusual 
length of the intestine of the porpoise with the provision of an extended absorbing 
surface in compensation for the absence of villi from its lining mucous membrane. 
Transverse sections made at intervals along the entire length of the tube revealed the 
presence of eight or nine longitudinal and projecting folds which occupied the greater 
part of the lumen. These left very little free lumen, and in those places where the bowel 
was firmly contracted, the cut face appeared almost solid by reason of the longitudinal 
projections. In the first half or thereby of the bowel, these projections were fairly 



326 DRS HEPBURN AND WATERSTON ON THE 

evenly distributed round the interior of the tube (PL III. fig. 8a), but in the lower 
or hinder half those upon the mesenteric side of the gut were considerably reduced in 
size to make room for an increased prominence of those upon the side opposite to the 
mesentery (PL III. fig. 9a). 

The microscopic appearances of the mucous membrane differed considerably in the 
upper and lower parts. At no point were villi discovered, but in the upper or anterior 
half the glandular arrangements were almost exactly similar to those of the duodenal 
mucous membrane (PL III. fig. 8b), except that in the bowel the glands were somewhat 
shorter than in the duodenum. Chalice cells were also prominent appearances. In the 
lower part of the bowel, the first noteworthy feature was the difference in the size of 
those ridges attached on the side next to the mesentery, as compared with the size of 
those on the side opposite to the mesentery. The latter set consisted of four thick and 
long projections. They occupied half of the circumference of the tube by their bases, 
but their projecting ends filled considerably more than half of the interior. The mucous 
membrane which lined the entire tube was very similar to that which has already been 
described for the upper part of the bowel, but the number of chalice cells now so greatly 
preponderated that the mucous membrane appeared like a network. The outstanding 
feature of the sections was the presence of globular masses of lymph tissue situated in 
the submucous layer (PL III. fig. 9b), but sending prolongations through the mucous 
covering apparently to discharge upon the free surface. We did not find a layer of 
epithelium covering those lymph nodules, but, as in other parts of the bowel, it may 
have been desquamated. This disposition of lymph tissue was confined to the three 
trenches which separated the four large ridges from each other, and these lymphoid 
patches were strictly limited to one side of the intestine, and no similar arrangement 
occurred on the mesenteric side of the intestinal wall. Nine or ten of these lymphoid 
masses were visible on the sides of a single ridge in each microscopic section, and the 
total amount of lymph tissue thus arranged must have been very great. 

The pancreas, lying between the liver and stomach, was pyramidal in shape, 
measuring 8 cms. transversely, 7 cms. antero-posteriorly, and 6 cms. in height. The 
base was posterior, and looked towards the lesser sac, while the blunted apex was in 
contact with the under surface of the liver. 

The left side was in contact with the first chamber of the stomach, the dorsal surface 
with the dorsal abdominal wall, but covered by peritoneum ; the right surface was in 
contact with the terminal part of the stomach, pylorus, and duodenum ; and the anterior- 
surface, continuous with the right surface, looked towards the lesser sac, and was crossed 
by the tubular part of the stomach. 

The tissue of which the gland was composed was folded round the bile-duct, which, 
therefore, passed through the gland. 

The liver had two large lobes — right and left — which were prolonged anteriorly into 
two conical projections, between which there was a triangular depressed area, mesial in 
position. 



SHAPE AND STRUCTURE OF ALIMENTARY VISCERA OF PORPOISE. 327 

These two projections coincided with the hollowed-out bases of the lungs, while 
the heart occujjied the mesial depression, the diaphragm intervening in both cases. 

There was no gall-bladder, and therefore no quadrate lobe to the liver, but indica- 
tions of a spigelian and a caudate lobe have already been noted. 

The microscopic structure of the liver, spleen, and pancreas did not materially differ 
from the appearances of those organs in man. The sections of the pancreas displayed 
the characteristic cells associated with acini and ducts. 

From an examination of the sections, we are inclined to think that the cells described 
as "central acinar cells" are merely sectional views of the cells which line the com- 
mencement of ducts that chance to lie upon the side of the section next to the observer ; 
and further, that the so-called paranucleus or "nebenkern" results from the same struc- 
tures lying on the side farthest from the observer, and therefore less distinct. Otherwise 
it seems that in such clear and distinct sections these special structures should appear 
more frequently than they do. 

It ought to be recorded that the tape-worm — Bothriocephalus latus — was found in 
the intestine. This parasite has not hitherto been observed in the alimentary canal of 
a marine mammal. 

Conclusions. 

(1) Although the porpoise, like other cetacea, is a mammal without hind limbs, 
and although its innominate bones are reduced to a couple of slender rods, yet, in 
the peritoneal arrangements associated with the posterior end of the abdominal 
cavity, there is evidence of a pelvic cavity which has not hitherto been recognised as 
such. 

(2) From the present observations, we agree with those previous observers who 
have described the stomach of the porpoise as four-chambered, and we are in harmony 
with them as regards the homologies of the first and second compartments, although 
we regard the first compartment as developed from the primitive stomach, and not as a 
dilatation of the post-diaphragmatic oesophagus. 

(3) We do not regard the " canal " or mural " passage," which lead onwards through 
the wall of the second compartment, as the third compartment, but look upon this 
" canal " as the inevitable association of the thick wall of the second compartment. 
Moreover, it is not quite so long as the " passage " of communication between the first 
and second chambers, and but little longer than the pyloric "passage," neither of which 
have ever been regarded as homologous with separate compartments. 

(4) We find the third compartment in a distinct chamber beyond the wall of the 
second, and clearly demarcated from the fourth, both by its somewhat spherical shape 
and by its constricted outlet. 

(5) Although Jungklaus and other writers support the view that the third com- 
partment of the adult porpoise is the mural " canal " or " passage " already referred to, 



3^8 DRS HEPBURN AND WATERSTON ON THE 

yet, in his plate, Jqngklaus figures several stomachs of foetal porpoises which apparently 
entirely agree with our description of the adult stomach. 

We are therefore forced to conclude that, by our method of preservation, we have 
been able to retain the normal appearances and shapes of these stomach chambers, 
which have hitherto either been lost, or of such uncertain characters as to lead to error 
or difficulty in the determination of their true homologies. 

(6) The fourth compartment, being tubular or cylindrical, is distinctly marked off 
from the spherical third chamber on the one hand, and from the duodenum on the 
other. The acute bend near the middle of this chamber, and the pre-pyloric dilatation 
(Antrum pylori), show how readily it might be still further subdivided. 

(7) From these considerations, it would seem as if the stomachs of all cetacea were 
constructed upon a common plan of subdivision into a series of chambers, with such 
variations as regards the number, size, and particular shapes of the compartments as 
are explicable by reference to the porpoise, and are probably due to differences in the 
characters of the teeth and the nature of the food determining the presence or absence 
of that particular compartment which we have called the "kau-magen" or masticatory 
stomach, and which in the case of the porpoise forms the first of the series of compart- 
ments. Further, the homologies of these compartments among different members of 
the Cetacea should be established by their structure and anatomical relations rather 
than by numerical sequence. 

(8) We regard the duodenum as that dilated part of the alimentary canal between 
the pylorus and a point immediately beyond the common entrance of the bile and 
pancreatic ducts. 

(9) Intestine proper commences at the termination of the duodenum, and is sus- 
pended throughout in the mesial peritoneal mesentery. 

(10) The small size of the spleen is probably compensated for by the unusual 
amount of lymphoid tissue distributed in the omentum and at different parts in the 
wall of the alimentary canal, especially towards its lower end. 

(11) Throughout the entire length of the alimentary canal, villi were absent. 



LITERATURE. 



The literature on the Cetacean Stomach is very extensive, but it has been brought up to date by Dr 
Friedrich Jungklaus, who quotes 63 memoirs in his paper " Der Magen der Cetaceen," Jenaische Zeitschrift 
fur Naturwissenschaft, xxxii., 1898. 

Lehrbuch der Vergleichenden MifcrosJcopischen Anatomie der Wirbeltiere, Oppel (Jena), 1896. 




SHAPE AND STRUCTURE OF ALIMENTARY VISCERA OF PORPOISE. 



329 



EXPLANATION OF FIGURES. 

Fig. 1. Inlet of pelvic cavity of male porpoise (viewed from abdominal cavity). 

Fig. 2. The hinder part of the abdominal cavity viewed from the side, showing inlet of pelvic cavity. 

Fig. 3. Section of first compartment of stomach of porpoise stained in hsematoxylin-eosin. x 96. 

Zeiss, oc. 4, obj. bb. 
Fig. 4 (a). Outline of section of second compartment of stomach of porpoise, x 20, to show thickness of 

mucous membrane. 
Fig. 4(b). Section of second compartment of stomach of porpoise stained in Benda's fluid. x 270. 

Zeiss, oc. 4, obj. dd, to show structure of secreting tubules. 
Fig. 5. Section of third compartment of stomach of porpoise stained in hsematoxylin-eosin. x 96. 

Zeiss, oc. 4, obj. bb. 
Fig. 6. Section of a tubule (deep end) of third compartment stained in hsematoxylin-eosin. x 270. 

Zeiss, oc. 4, obj. dd. 
Fig. 7A. Section of fourth compartment stained in hsematoxylin-picro-fuchsin. x 96. Zeiss, 

oc. 4, obj. BB. 
Fig. 7B. t.s. of one tubule. x 470. Zeiss, oc. 4, obj. e. 
Fig. 8. t.s. section of upper end of intestine stained in eosin-methyl-blue. (a) natural size, (b) x 96. 

Zeiss, oc. 4, obj. bb. 
Fig. 9A. t.s. of lower end of intestine, natural size. 
Fig. 9B. One ruga in transverse section stained in hsematoxylin-eosin. x 20. Zeiss, oc. 4 : Beck, 

obj. 2". 
Fig. 10. Scheme of compartments of stomach of porpoise. 



A. After Jungklaus. 



B. Hepburn and Waterdon. 



0. (Esophagus. 


O. GEsophagus. 


I. First compartment. 


I. First compartment (Kaumagen). 


G. Epithelial boundary between first and 


II. Second ,, 


second compartments. 


III. Third 


II. Second compartment. 


IV. (a) Proximal part of fourth compartment. 


III. Third 


(b) Distal „ „ „ 


IV. Fourth 


(c) Antrum pylori. 


P. Pylorus. 


P. Pylorus. 


Ad. Ampulla duodenalis. 


D. Duodenum. 


P.v. Papilla vateri. 


P.v. Common entrance of bile and pancreatic 


D. Duodenum. 


ducts, Papilla vateri. 




Int. Intestine. 



We desire to express our indebtedness to Sir Wm. Turner and Professor Schafee 
r much friendly criticism arid suggestion during the preparation of this paper. 



TRANS. ROY. SOC. EDIN., VOL. XL. PART II. (NO. 16). 



3c 



)c Edm r 



Hepburn and Waterston: Alimentary Viscera of the Porpoise-Plate I. 



Vol XL 



Urinary Bladder 



Left Testis 




Right Testis 



Intestine [cut) 
Vasn deferent in 

Fiff.l. INLET OF PELVIC CAVITY OF MALE PORPOISE VIEWED FROM ABDOMINAL CAVITY. 



Urinary Bladder 



Vasa deferent i a 



eft Testes 
id outwards) 




Right Kidney 
Intestine {cut) 



Left Kidney 



Fig. 2. THE HINDER PART OF THE ABDOMINAL CAVITY VIEWED FROM THE SIDE. 



1 . DEL. AD NAT. 



W. GRIGGS, LITH. 






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Hepburn and Waterston: Alimentary Viscera of the Porpoise-Plate II. 



Vol XL. 





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Fig. 4(B). 






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HEPBURN AND WATERSTON : ALIMENTARY VISCERA OF THE PORPOISE-PLATE III. 




Vol. XL. 



W. GRIGGS. UTH. 



( 331 ) 



XVII. — On the Primary Structure of certain Paleozoic Stems with the Dadoxylon 
Type of Wood. By D. H. Scott, M.A., Ph.D., F.E.S., Hon. Keeper of the 
Jodrell Laboratory, Koyal Botanic Gardens, Kew. Communicated by Professor 
I. Bayley Balfour, F.R.S. (With Six Plates.) 

(Read January 6, 1902. Issued separately April 7, 1902.) 

In a Note published in the Annals of Botany for December 1899,* I gave some 
account of the structure of two stems from the Lower Carboniferous of Scotland, 
provisionally named Araucarioxylon fasciculare, sp. nov., and A. antiquum, Kr. 
(Witham, sp.). 

In the present paper these stems are described fully, with the help of illustrations, 
and others, presenting similar points of interest, are added. The species dealt with are 
the following : — 

Calamopitys fascicidaris (Araucarioxylon fasciculare of the Note). 
Calamopitys beinertiana (Araucarioxylon beinertianum, Kr.), (Gopp., sp.). 

Pitys antiqua, Witham (Araucarioxylon antiquum, Kr. of the Note). 
Pitys Withami (Pinites Withami, Lindl. & Hutt.). 
Pitys primazva, Witham. 

Dadoxylon Spenceri, sp. nov. 

The reasons for the nomenclature adopted will be given in each case when the 
structure has been described. It was stated in the Preliminary Note that the two 
stems there described would certainly require generic separation on the basis of their 
primary characters (I.e., p. 619). This has now been done, but I have succeeded in 
avoiding the creation of any new genus, for in the one case the characters appeared to 
indicate the genus Calamopitys of Unger as the appropriate one, while in the other the 
use of Witham's old generic name, in an emended sense, seemed to meet the case. 

Where the old genus Dadoxylon or Araucarioxylon has to be kept up, I agree 
with Knowlton t and Zeiller \ that the former name is to be preferred in the case of 
Palaeozoic woods, restricting Araucarioxylon to Secondary or Tertiary specimens, which 
may more probably be referred to true Araucariese. The use of the name Araucari- 
oxylon for Palaeozoic specimens, probably belonging to the Cordaitese, or to 
some other family equally remote from true Araucariese, is likely to mislead, and 
though I employed this name in the Preliminary Note, I now think it better to 
avoid it. 

* " On the Primary Wood of certain Araucarioxylons" Ann. Bot., vol. xiii. p. 615. 

t " A Revision of the Genus Araucarioxylon of Kraus," Proc. U.S. Nat. Mus., vol. xii. p. 601, 1890. 

X Elements de Pattobotanique, p. 279, 1900. 

TRANS. ROY. S0C. EDIN., VOL. XL. PART II. (NO. 17). 3 d 



332 DR D. H. SCOTT ON THE 

The importance of the fossils now to be described consists in their showing the 
primaiy structure of the wood ; in all of them there is proof of the existence, within 
the zone of secondary wood, of distinct strands of primary xylem, resembling more or 
Jess closely those which have long been known in the stems of the Lyginodendrese and 
Poroxylese. This structure co-exists with secondary wood of the Dadoxylon type, in 
some cases agreeing exactly with the wood which is known to have belonged to the 
stems of Cordaitese.* Thus these fossils tend to establish a connection between the 
stems of Palaeozoic Gymnosperms and those of certain Cycadofilices, and so to throw new 
light on the question of the Filicinean origin of the Gymnospermous Phanerogams. 
The subject of the course of the leaf-traces is closely connected with that of the primary 
wood-strands, and is dealt with below so far as the material afforded data. Other 
characters are considered incidentally. At the close of the paper the theoretical 
bearings of the structural features in question are discussed. 

I. Calamopitys, Unger. 

1. Calamopitys fascicular is, sp. n. 

This is the stem described in my Note of 1899 under the provisional name of 
Araucarioxylon fasciculare. The reasons for now placing the fossil in Unger's genus 
will become apparent when the structure has been described. As mentioned in the 
Preliminary Note, two specimens have been examined ; the first which came under 
investigation is in the collection of Mr Kidston, and was found in 1898 by Mr John 
Renwick at the Loch Humphrey Burn in the Kilpatrick Hills, Dumbartonshire. The 
horizon is that of the Calciferous Sandstone Series. Mr Kidston very kindly placed 
his sections at my disposal for investigation, and also allowed me to have some 
additional sections cut from the remainder of the block. 

The second specimen is one of which the sections are preserved in the Williamson 
Collection under the generic name Dadoxylon. The structure is identical with that of 
Mr Kidston's stem (cf. PL I. phot. 1 and PI. III. fig. l). The Williamson specimen is 
described in his MS. catalogue as being derived from the Carboniferous Limestone near 
Haltwhistle. Thus both specimens are of Lower Carboniferous age. This plant, like the 
other species to be described, combines an Araucarian type of secondary wood with the 
presence of distinct primary strands of xylem around the pith. It is characterised by 
the small diameter of the pith, the small number and relatively large size of the primary 
xylem-strands, the simple leaf-traces, and the narrow medullary rays, giving the 
secondary wood a Cordaitean character. 

The diameter of the pith is only about 2 mm. in Mr Kidston's specimen, and about 
3 mm. in the Williamson example. The whole specimen reaches a maximum diameter 

* On the Cordaiteae, see Grand' Eury, Flore carbonifere du Departement de la Loire, 1877 ; Renault, Structure 
compare de quelques Tiges de la 'Flore carbonifere, 1879 ; Cours de Bot. Fossile, t. i., 1881. A general account of the 
family is given in Solms-Laubach's Fossil Botany, chap, v., Eng. trans!., 1891, and in my Studies in Fossil Botany, 
Lecture XII., 1900. 



PRIMARY STRUCTURE OF CERTAIN PALEOZOIC STEMS. 333 

of nearly 3 cm. in the former, and about 2 cm. in the latter, but these dimensions are 
of no significance, as the wood is manifestly incomplete. In neither specimen is anything 
beyond the wood preserved. 

In Mr Kidston's specimen the pith is complete, though somewhat contracted (see 
fig. 1) ; consequently all the xylem-strands can be recognised, and their course traced 
in successive transverse sections. In the Williamson stem the pith has perished, and 
the smaller xylem-strands are obscure ; for details of the w T ood and larger primary 
strands, however, this specimen is rather superior to the other. Fig. 1, from one of the 
transverse sections of Mr Kidston's specimen, gives a good idea of the general structure. 
The parenchymatous pith, which, owing to shrinkage, has partly separated from the sur- 
rounding wood, has, in itself, a very uniform structure ; the peripheral cells are narrower 
and have rather thinner walls than those towards the centre (compare the longitudinal 
section in fig. 3) ; some of the larger elements are filled with dense carbonaceous contents, 
which may indicate that they had a secretory function during life. Around the pith a 
number of xylem-strands are disposed, forming an irregular ring. Eight of these strands 
are wholly or partially embedded in the pith ; a ninth strand (B), much the largest of 
all, is passing out into the zone of wood. It is a constant rule, holding good for all the 
sections of both specimens, that the outgoing bundles are those which attain the maximum 
dimensions (cf. phot. 2, from the Williamson specimen). A, the next largest strand, 
is in close contact with the secondary wood, and will be the next to pass out above, as 
is shown by the comparison of successive transverse sections. Most of the smaller 
strands are actually embedded in the pith, and are separated from the inner edge of the 
wood by several layers of parenchyma (cf. the longitudinal section, fig. 3). We have 
here an approach to a condition which we shall find existing, in a much more marked 
degree, in Pitys antiqua. 

There are in all eight transverse sections of Mr Kidston's specimen. They were cut 
at different times, and I have no record of their order, but have been able to deter- 
mine it with practical certainty by careful comparison of the peculiarities of the 
individual sections as to detailed structure, position and form of cracks, exact state 
of preservation, etc. The succession of the sections having been thus ascertained, 
it became possible to determine the course of the xylem-strands. The camera lucida 
diagrams in the text, 1 to 4, prepared for me by Mr L. A. Boodle, F.L.S., are taken 
from a series of four consecutive sections, sufficient to fix the essential points in the 
distribution of the strands. The series is from above downwards. The top section 
of the four (diagram l) shows three principal bundles, markedly larger than the rest. 
One of them, C, is still far out in the secondary wood ; another, B, of equal or even 
greater size, has just reached, with its inner edge, the periphery of the pith ; the third, 
A, which is much smaller, though still far exceeding the other circum-medullary strands 
in size, has already entered the pith. These three leaf-traces may be taken as fixing 
the position of the three orthostichies, A, B and C, on which the leaves supplied by 
these traces were inserted. A, being cut lowest down in its course, belongs to the 



334 



DR D. H. SCOTT ON THE 



uppermost leaf of the three, B to the next, and C to the lowest. In the next section 
(diagram 2) the same three orthostichies are represented. The bundle C has here moved 
up nearly to the pith, but is still separated from it by a mass of radially arranged 
parenchyma. B has moved but little inwards, and has scarcely changed. A is much 
smaller than before, and has shifted in watch-hand direction, approaching an adjacent 
small strand (a) on that side. In the next section below (diagram 3) a new bundle, D, 
makes its appearance out in the wood, between A and B ; it evidently comes from a 
leaf next below C, and thus gives the position of a new orthostichy. C has here just 
reached the edge of the pith and B is projecting further into it. A is now scarcely 




DlAGKAM 1 (K. 788). 

larger than its fellow circum-medullary strands ; it has shifted a little further and is now 
joining the adjacent strand, a ; it has also become embedded in the tissue of the pith. 

In the lowest section of the series (diagram 4) a new strand again, E, is entering 
through the wood on the left, between B and C, thus fixing the position of the fifth 
orthostichy, and clearly belonging to the lowest of the five leaves which are represented 
by their traces in this series. D has here reached the edge of the pith ; C is beginning 
to enter it, and is somewhat reduced in size ; B is much smaller than before, and has 
entered the pith sufficiently to have been drawn away from the wood by the contraction 
of the former. A, no longer distinguished by size, is still fusing with the adjacent 
strand, a. 

The whole arrangement clearly points to a 2/5 phyllotaxis. The three successive 
traces, which are alone recognisable in diagrams 1 and 2, are separated by angles which 



PRIMARY STRUCTURE OF CERTAIN PALAEOZOIC STEMS. 



335 



correspond roughly to a 2/5 between A and B, and B and C, and about 1/5 between 
C and A. Where a new trace, D, makes its appearance (diagram 3) it bisects the 2/5 
gap A — B, and again where a fifth trace, E, appears (diagram 4) it bisects in like 
manner the other 2/5 gap, B — C. It may be mentioned that all the leaf- traces shown 
in the other sections, not figured, are likewise referable to the same five orthostichies, 
A, B, C, D, E, and follow the same order of succession. No other than a 2/5 arrange- 
ment would account for the facts. The irregularities in divergence which occur are 
easily explained by the distortion due to cracks, and to the contraction of the pith. 

The course of the smaller strands, i.e., of the lower ends of the leaf- traces where 
they have become medullary, has not been completely made out, but some light has 

C 




Diagram 2 (K. 628). 

been thrown on it. Thus the entering leaf-trace A, after it has become embedded in 
the pith and has diminished much in size, obviously united with the adjoining bundle 
(a) on the kathodic side (diagrams 3 and 4). The arrangement of the strands indicates 
that this was a general rule. The last leaf-trace to enter, above A, would have lain on 
the orthostichy E. In this position we see, in diagram 1, two small bundles (e) which may 
well be the reduced leaf-trace with its reparatory strand. Lower down (diagram 3) these 
two bundles are fusing, and in the lowest section (diagram 4) they are completely fused. 

The leaf-trace still further above would have been on the orthostichy D. Two 
small bundles in this position (d) are already uniting in the uppermost section (diagram 
l), and in the next below (diagram 2) their union is complete. 

Considering next the leaf-traces which enter below A, the small strand b on the 



336 



DR D. H. SCOTT ON THE 



kathodic side of B is presumably the one destined to unite with that leaf-trace 
(diagrams 1-3) ; in the lowest section (diagram 4) it has disappeared, which may be 
due to its fusion with B, or more probably to mere destruction of tissue ; for the fusion, 
according to the analogy of other strands, would not be likely to take place so high up. 
Lastly, the remaining small bundle, c, which appears in all four sections, is in all 
probability the reparatory strand ready to unite with C, which it is already approaching 
in the lowest section (diagram 4). In other words, if we trace the course of the 
bundles from below upwards, we may say that each circum-medullary strand branches 




Diagram 3 (K. 629). 

at regular intervals ; the one branch, that on the anodic side, becomes the leaf-trace 
and passes out, while the other continues its course up the stem as a reparatory strand, 
until the next leaf of the orthostichy has to be supplied. It is, however, probable that 
subsidiary unions between the bundles also occurred. 

The course of the bundles, so far as it has been determined, thus appears to be 
identical with that found in the stem of Lyginodendron oldhamium* 

The position of the xylem-strands in the three transverse sections of the Williamson 
specimens also points to a 2/5 phyllotaxis. The order of the sections from above 
downwards appears to be : — 1378, 1380, 1379. 

The internodes of the stem were probably short, as is indicated by the rapid succession 

* Williamson and Scott, " Further Observations on the Organization of the Fossil Plants of the Coal-Measures." 
Pt. III. Lyginodendron and Heterangimn, Phil. Trans. Roy. Soc, vol. 186 (1895), B, p. 711. 



PRIMARY STRUCTURE OF CERTAIN PALAEOZOIC STEMS. 



337 



of the outgoing leaf-traces. Sometimes, as shown in diagram 3, as many as three 
successive traces, passing out through the wood, are seen in the same transverse section. 
In the lower part of its course, as we have seen, the leaf- trace bundle passes very 
gradually outwards, diverging but little from the vertical direction. When it has once 
fairly entered the wood, however, it curves more rapidly (owing to the growth in thickness 
of this zone), so as to assume a more nearly horizontal course, and is consequently cut 
in an approximately transverse plane when intersected by a tangential section of the 
wood ; such a section, from the Williamson specimen, is represented in PI. IV. fig. 7. 
From the course of these strands, as described above, there can be no doubt that 




Diagram 4 (K. 540 c ). 

they represent the leaf-traces, or rather their xylem-constituent, passing out to leaves 
with a 2/5 phyllotaxis. On a superficial view, it might perhaps be supposed that the 
larger strands belonged to branches, but more careful observation shows every grade of 
transition between the larger and smaller strands, and proves their identical nature 
(see diagrams 1-4, and figs. 1 and 2). It is evident that the bundle, as it approached 
its point of exit from the pith, increased rapidly in size, attaining its full dimensions 
where it began to pass outwards. A similar increase in size, though perhaps less 
striking, occurs in the outgoing strands of Lyginodendron * and Poroxylon.f 

The structure of the primary xylem-strands is most obvious where they attain their 



* Williamson and Scott, loc. tit., PL 21, fig. 1. 

t Bertrand et Eenault, " Recherches sur les Poroxylons," Arch,. Bot. du Nord 
tigs. 198, 199, etc. 



la France, 3 me Annee, 1886, 



338 BR D. H. SCOTT ON THE 

largest dimensions. The general contour is here nearly circular, and the smallest 
elements are placed near the centre, where they form a small group, accompanied by a 
little parenchyma (phot. 2, fig. 1, B). In some bundles the small elements form 
two distinct groups, separated by parenchyma ; this is found chiefly where the strand 
is well advanced on its outward course, as for example in that shown in fig. 7, from a 
tangential section, where the strand is seen passing through the secondary wood. 
Oblique sections show that the small central tracheides are spirally thickened ; I have 
not seen a satisfactory longitudinal section through one of the larger strands, but in 
the small bundle represented in radial section in fig. 3, the spirals in the interior of the 
strand are evident. As regards the large strands, there can be no doubt that the 
structure is mesarch, the protoxylem lying about at the centre of the whole strand, and 
probably separating into two groups as the bundle passed outwards. The tracheides 
towards the periphery of the primary strand have pitted walls, like those of the 
secondary wood, but are of larger size, reaching a diameter of 0*1 mm. or more. 
Between these large elements and the central protoxylem, transitional, scalariform or 
reticulate forms of sculpturing occur. 

As the xylem-strand is followed downwards at the margin of the pith, it rapidly 
diminishes in size, and its elements become smaller (see A in fig. 1). Lower down, 
the strand passes deeper into the pith, so as to become separated from the inner margin 
of the secondary wood by a few (about 2-6) layers of parenchyma (fig. 1). In the 
lower part of its course, the arrangement of the elements of the bundle undergoes some 
change ; the larger tracheides come to be limited to the outer side of the strand, and the 
spiral elements lie further inwards. A good example of a bundle fairly low down in 
its course is shown, in transverse section, in fig. 2. The structure is still mesarch ; the 
protoxylem, however, is beginning to approach the inner edge of the strand ; the xylem 
is interrupted at several points by parenchymatous elements. The small strand shown 
in radial longitudinal section, in fig. 3, has its spiral elements much nearer the inner 
than the outer side. 

A similar structure is seen in some of the smaller bundles in the transverse section 
represented in fig. 1. Thus, as the bundle is traced downwards, the centripetal part of 
the xylem diminishes, but it does not appear that a purely endarch structure was ever 
attained. In the bundles of Poroxylon, according to Messrs Bertrand and Eenault, 
the centripetal xylem disappears altogether towards the lower end of each bundle.* 
The change of structure in Calamopitys fascicularis is in the same direction, but has 
not gone so far. 

Broadly speaking, the secondary wood has the same structure as in the stem of a 
Cordaites ; the medullary rays are narrow, and the pitting of the tracheides is of the 
usual Araucarian type. The structure is well shown in the radial section represented in 
fig. 4, where the pits are seen to be arranged in three or four rows on the radial walls. A 
small part, represented more highly magnified in fig. 5, shows the hexagonal bordered 

* hoc. cit., p. 306. 



PRIMARY STRUCTURE OF CERTAIN PALEOZOIC STEMS. 339 

pits, with the narrow, slit-like, more or less inclined pore, very clearly. The borders of 
the pits are sometimes beautifully shown in section, where the wood is cut tangentially, 
as represented in PL IV. fig. 6 (b.p.), from the Williamson specimen. 

The medullary rays, which have the usual muriform arrangement of their elements 
(fig. 4), are, for the most part, one cell only in thickness, but often become two cells 
thick in places (see figs. 6 and 7). Some are of considerable height (up to sixteen 
cells or more), while others are only one or two cells high (fig. 6). The outgoing leaf- 
trace is accompanied by a considerable amount of parenchyma, especially on the upper 
side* (fig. 7). The medullary rays in the neighbourhood of the leaf-trace are irregular, 
and generally shorter and broader than elsewhere. 

The pits adjacent to the medullary rays are bordered only on the side towards the 
tracheide — the usual structure in all such cases (see fig. 6, m.r.). 

The chief peculiarity of. the secondary wood is in its innermost region, near the pith, 
where the elements have an unusual form and arrangement. The tracheides here are 
broad and short, often with horizontal terminal walls, which thus appear in surface 
view when seen in a transverse section (cf. figs. 2 and 3). Their course is tortuous and 
irregular ; the maximum diameter is usually in the radial direction (see figs. 2 and 3). 
The pits on their walls, though in more numerous series than elsewhere, are of the 
usual form ; the arrangement of the tracheides, so far as any regularity can be traced, 
is in radial series, and the medullary rays pass between them ; towards the exterior 
the structure passes over rapidly into that of the normal wood. This peculiarity of the 
inner zone of wood is common to both the specimens investigated. There seems to be 
no doubt that the short tracheides in question belong to the secondary wood ; they 
resemble the primary tracheides found by Mr Seward in his new genus Megaloxylon,^ 
and may probably have served, as he believes to have been the case in that plant, 
for the storage rather than for the conduction of water. 

The chief results arrived at from the investigation of Calamopitys fascicularis are 
the following : — 

(1.) The small pith (2-3 mm. in diameter) is surrounded by a ring of distinct 
primary xylem-strands, eight or nine in number, with mesarcb structure. 

(2.) These strands are the xylem-constituent of the leaf-traces ; they attain their 
maximum diameter ("8 mm.-l mm.) when they are about to leave the pith and to pass 
out through the secondary wood. Below this point they rapidly diminish in diameter, 
and each unites with the adjacent strand on its kathodic side. 

(3.) The outgoing strands are arranged on five orthostichies, corresponding to a 2/5 
phyllotaxis. In passing through the wood, each leaf-trace is represented by a single 
strand. 

(4.) The secondary wood has the typical Araucarian or Cordaitean structure, with 

* The orientation of fig. 7 lias been determined by comparison with a transverse section of the same specimen, in 
which the parenchyma accompanying a leaf-trace is found on the inner (= upper) side of the strand. 

t Seward, " Notes on the Binney Collection of Coal-Measure Plants." Part II. Megaloxylon- Proc. Cambridge 
Phil. Hoc., vol. x, 1899, p. 158. 

TRANS. ROY. SOC. EDIN., VOL. XL. PART II. (NO. 17). 3 e 



340 DR D. H. SCOTT ON THE 

medullary rays one, or at most two cells in thickness. The inner part of the wood 
consists of short broad tracheides, with a tortuous course. 

The reasons for placing this species in the genus Calamopitys of Unger may now be 
briefly considered. This genus was established by Unger on the species C. Saturni in 
1856, # but our present accurate knowledge of its structure is due entirely to the 
recent work of Count SoLMS-LAUBACH,t who has further shown that Unger's Stigmaria 
annularis was also a Calamopitys, scarcely distinct from the original species. The 
generic name Calamopitys, which expressed Unger's view of the Calamarian affinities 
of his fossil, is entirely inappropriate, and the real relationships of the genus have 
proved to lie in quite a different direction. The old name is kept up simply in order 
to avoid burdening the synonymy with a new one. 

In the specimens of Calamopitys Saturni there is a small pith (only about 1-2 mm. 
in diameter) surrounded by an irregular tracheal zone, reduced or perhaps wholly inter- 
rupted at certain points, and forming enlarged nests between them, each such nest 
having a central group of small elements, presumably the protoxylem. This zone of 
primary xylem is surrounded by the secondary wood, the tracheides of which have small 
narrow circular pits ranged in several rows on their radial walls. The medullary rays 
are usually pluriseriate. Some remains of the phloem have been found, and the cortex 
is well shown ; in its inner part it consists of parenchyma, while towards the periphery 
it contains parallel bands of hypodermal fibres, thus having the well-known ' Sparganum ' 
structure. In the cortex the leaf-trace bundles are also found ; their course has been 
followed with great completeness, in successive transverse sections, by Count Solms- 
Laubach, who finds that a single bundle leaves the wood, and at first (as in Lygino- 
dendron) is accompanied by secondary xylem. The leaf-trace divides into two on 
entering the cortex, then into four, and finally into six ; the six resulting bundles enter 
one of the leaf-bases which are found attached to the stem. The leaf-stalk has the 
structure of Kalymma, and as Kalymma is known to have branched, the inference is 
that the leaves of Calamopitys were compound. Count Solms-Laubach has shown 
beyond doubt that the phyllotaxis was 2/5, or extremely near it. In the form 
referred to C. annularis, the primary wood is more extensive, and apparently more con- 
tinuous ; in some of the specimens the pith attains a diameter of 7 mm. In other 
respects there is no important difference between C. annularis and C. Saturni, and it is 
not even certain that the species were really distinct. Both forms belong to the Culm, 
or Lower Carboniferous, of Central Germany, and are thus of similar horizon to that of 
the British species. 

In comparing the German species of Calamopitys with our own fossil, we are 
unfortunately restricted to characters presented by the pith and wood, for these parts 
are alone preserved in the British specimens. Count Solms-Laubach most kindly lent 

* Richter u. Unger, Beitrag z. Palxont. d. Thiiringer W aides, Denkschr. d. K. K. Alcad. zu Wien, math, naturw. CI. 
Bd. xi., 1856. 

t Pflanzenreste des Unterculm v. Saalfeld in Tliiiringen — Abh. d. K. Preuss. Geol. Landesanstalt, Heft 23, 1896, p. 63, 
Taf. IV. 



PRIMARY STRUCTURE OF CERTAIN PALAEOZOIC STEMS. 341 

me some sections of C. annularis for comparison with our own, and on visiting 
Strasburg I was able to examine a number of other sections both of that species and of 
C. Saturni. Neither of the German fossils is specifically identical with the British 
form, but I could find no grounds on which to base a generic distinction. A small 
specimen of C. annularis closely resembled Mr Kidston's specimen of C. fascicularis 
in the character of its tissues, and might, on superficial examination of the sections, 
have been taken for a part of the same stem. It differed, however, in the more 
continuous primary xylem, and the less marked enlargement of the outgoing xylem- 
strands, as compared with the others. In this specimen the rays were usually two cells 
thick, but often one cell only in thickness near the pith. There was thus little differ- 
ence in this respect from the British form. In the large specimens, both of C. 
annularis and C. Saturni, the rays are wider. The pith appeared to present no 
marked difference from that of C. fascicularis. Count Solms-Laubach has pointed out 
that in C. Saturni a xylem-strand is sometimes found embedded in the pith, without 
direct contact with the secondary wood, though not far removed from it (loc. cit., p. 72). 
I have observed the same thing in one of his sections of C. annularis, and this, as we 
have seen, is characteristic of all the smaller xylem-strands in our C. fascicularis. C. 
Saturni, in the greater separation of the individual circum-medullary strands, 
approaches nearer to our species than does the form C. annularis. The preservation of 
the Thuringian specimens is, however, such that the exact limits of the xylem-strands 
are much more difficult to make out than in the British fossil, especially Mr Kidston's 
specimen. In the shortness of the internodes C. Saturni also agrees with C. 
fascicularis, and, as we have seen, the phyllotaxis and general course of the xylem- 
strands were the same, so far as the evidence available can show. 

On the whole, taking into consideration all the characters available for comparison 
I feel no doubt that the genus Calamopitys is that in which our fossil may most 
naturally be placed. The form and relative dimensions of the xylem-strands, and the 
usually uniseriate rays, serve to characterise C. fascicularis specifically. 

2. Calamopitys beinertiana (Goepp. sp.). 

The investigation of this species is based on a specimen collected by Mr Kidston 
in September 1900 at Norham Bridge on the Tweed; the horizon (Calciferous Sand- 
stone Series) is similar to that of the Dumbartonshire specimen of C. fascicularis. Mr 
Kidston had numerous sections prepared by Mr Lomax from his specimen, and from 
these he himself determined the main points in its structure, and identified the species 
with the Araucarites beinertianus of Goeppert.* He then very kindly lent me the 
sections for further investigation, with a view to the inclusion of the species in the 
present communication. 

The specimen is a rather large one, about 4 cm. in diameter in its present incomplete 

* This identification has since been confirmed, as will be explained below, by comparison with authentic sections 
of A. heinertianus, for the loan of which I am indebted to Count Solms-Laubach. 



342 DR D. H. SCOTT ON THE 

state (see phot. 3) ; the main stem shows nothing outside the wood, and probably not 
the full thickness of that, but the transverse sections also contain a detached fragment 
which has the bark attached, though in a poor state of preservation. The main piece is 
fairly well preserved, but in places the tissues appear to have suffered from maceration 
before petrifaction took place. The most important region — the zone immediately 
surrounding the pith — is a good deal damaged, but the chief features of its structure 
are sufficiently plain, as the figures show. The pith, 13-15 mm. in diameter, has a very 
characteristic appearance, owing to the presence of conspicuous masses of dark-coloured 
cells, much resembling the ' sclerotic nests ' in the pith of Lyginodendron Old- 
hamium * (see phots. 3 and 4). The nests here consist of rather thick-walled cells, 
containing carbonaceous matter, which may probably have been derived from the 
disorganised inner layers of a cell- wall originally much thicker than it at present 
appears. In the middle of each nest there is a small irregular group of very dark 
cells ; the more peripheral elements of the nest are squarish cells, arranged in series 
radiating in all directions from the central group. These radial series are continued 
out into the surrounding thin-walled pith, and are no doubt the result of growth and 
cell-division subsequent to the first origin of the sclerotic nest. Such a structure is 
commonly met with in recent plants, around groups of hard tissue differentiated in the 
midst of an actively growing parenchymatous matrix. Similar cell-divisions occur 
around the sclerotic nests of Lyginodendron, but not to the same extent as in the 
present species. The general resemblance in the pith of the two plants is sufficiently 
striking. 

The most important point, however, is the presence of a number of primary xyl em- 
strands around the pith, adjoining the inner edge of the secondary wood. The bundles are 
small compared with the size of the pith, though some of them reach a diameter of about 
75 mm. (see PL IV. fig. 8). The larger strands are just entering the w T ood ; those which 
remain at the periphery of the pith are smaller (see fig. 9). It appears, therefore, that 
here, as in C. fascicularis, the strand attained its maximum size just before passing out 
towards a leaf. As would be expected from the large dimensions of the pith, the xylem- 
strands are numerous ; I was able, in spite of the imperfect preservation, to count seven- 
teen strands which were clear enough for the position of the protoxylem to be recog- 
nised. No doubt there were others besides, too obscure to be identified. In parts of 
the periphery of the pith the primary xylem appears to be almost continuous, for the 
inner edge of the wood is here formed of irregularly arranged tracheides, larger than 
those of the secondary zone. This lateral confluence of the primary xylem-groups, 
though not amounting to continuity all round the pith, recalls the structure found by 
Count Solms-Laubach in Calamopitys annidaris.f The primary strands of C. beiner- 
tianus bear a strong resemblance to those of C. fascicularis, as is evident if we compare 
the large outgoing xylem-bundle shown in fig. 8 with the corresponding large strands 

* Williamson and Scott, loc. cit., p. 717 ; PI. 18, phots. 1 and 4 ; PI. 21, fig. 1. 
t Loc. cit., p. 74. 



PRIMARY STRUCTURE OF CERTAIN PALEOZOIC STEMS. 343 

of the former sj:)ecies represented in fig. 1 and phot. 2 ; or again, if we compare the 
smaller xylern-strands of the two species (fig. 9 with fig. 2). In C. beinertianus, as in 
the former species, the outgoing strand has an almost circular transverse section, with 
the smallest elements towards the centre (fig. 8). As the strand figured is damaged at 
the back, we cannot be quite certain whether the structure was strictl} 7 mesarch, i.e., 
whether there were tracheides all round the protoxylem. From the evidence of another 
outgoing strand, however, it is probable that this was the case, so that the resemblance 
to C. fascicularis appears to be complete, so far as these larger strands are concerned. 
I have also carefully examined all the smaller xylem-strands shown in the transverse 
sections ; some of them, like the outgoing bundles, may be mesarch, but the majorit} 7 
are certainly endarch ; some have a structure which may be described as hippocrepi- 
form-endarch (see fig. 9) ; that is to say, the ring of tracheides is interrupted at the 
back of the bundle, so that on the side towards the pith the protoxylem is in contact 
with thin-walled tissue. There is very little real difference between this structure and 
that of the smaller mesarch strands of C. fascicularis (cf. fig. 2) ; there also the xylem, 
or rather the tracheal tissue, is interrupted, but not so regularly on the inner side of the 
strand. Similar differences occur amono; the bundles in the stem of Osmunda* 

This partial assumption of endarch structure is of interest, as marking the first step 
in that disappearance of centripetal xylem which characterises the later types of 
Gymnospermous stem. 

In some of the longitudinal sections the spiral tracheides of the protoxylem are 
quite distinct, as in the bundle shown in fig. 10. Here the protoxylem is adjacent to 
parenchyma, but the poorly preserved element still further to the interior is a tracheide. 
The section, however, as shown by the direction of the medullary ra} 7 s. was not accu- 
rately radial, so most probably this was a ' hippocrepiform endarch ' bundle, one of the 
flanking tracheides appearing on the inner side of the strand in consequence of the 
deviation of the section from the radial plane. The primary tracheides show the usual 
transitions through reticulate to pitted structure. The walls of the largest of the 
primary xylem-elements have numerous rows of hexagonal bordered pits, sometimes 
beautifully preserved (see fig. 11). The largest primary tracheides are as much as *1 mm. 
in diameter ; those of the secondary wood seldom exceed "05 mm. 

The pitting of the secondary wood, usually imperfectly preserved, but well shown 
at a few places, is limited, as usual, to the radial walls. The pits are most often in two 
rows only ; sometimes they are scattered, and even when in contact do not usually assume 
a regular hexagonal outline, though sometimes there is an approach to this form. The 
bordered structure of the pit with a narrow slit-like pore is evident in the better pre- 
served parts of the wood. Examples of medullary ra}^, as seen in tangential section, are 
shown in fig. 12. They are nearly always one cell only in thickness; cases where the 
ray is locally two or more cells thick (as in fig. 12, B) are very rare, and appear to be 
connected with some irregularity in the course of the tracheides. The great differences in 

* Zenetti, Bot. Zeitung, p. 57, woodcut 2, and p. 62, woodcut 3, 1895.. 



344 DR D. H. SCOTT ON THE 

the height of the rays are sufficiently illustrated by the comparison of figs. 12, A, and 
12, C. Small rays two cells in height are common, and rays only one cell high also occur. 
In the rays of greater height there is often considerable variation in the dimensions of 
the constituent cells (see fig. 12, A). The secondary wood, as a whole, has quite a Con- 
iferous character, and thus offers a striking contrast to the primary structure. 

In some of the tangential sections a large leaf-trace bundle, accompanied by 
parenchyma, is seen passing out through the wood (see PL V. fig. 13). The strand 
is rather obscure, as it is cut obliquely ; the smallest elements are central, with some 
xylem and parenchyma next them, and the structure therefore probably mesarch. The 
pits on the larger tracheides of the strand can be recognised. It is important to note 
that in this part of its course the leaf-trace is represented by a single strand and not 
by a pair of bundles, thus agreeing with C. fascicularis. 

The fragment of stem with bark attached has been already mentioned. The bark, 
which is about 5 mm. thick, is shown in transverse section, and consists of alternate 
darker and lighter tangential bands of tissue. The whole mass evidently represents a 
regular scale-bark ; in some of the darker bands radially arranged peridermic cells can 
be recognised ; the intermediate softer tissue may be partly phloem ; the larger cells 
to the outside between the periderm-bands may have belonged to the primary cortex. 
At one place a broad band of thick-walled periderm is well preserved ; at another, 
a few displaced fibres can be recognised ; but, on the whole, the preservation is too 
imperfect to justify a more detailed description. 

As mentioned above, the specimen just described was identified by Mr Kidston with 
the Araucarites beinertianus of Goeppert,* with which the characters of the secondary 
wood agree, as shown by Goeppert and Stenzel's diagnosis (1888). " Ar[aucaria3] 
ligni, stratis concentricis haud conspicuis, tracheidis amplis punctatis, punctis 1-, 2-, 
rarius 3-serialibus spiraliter dispositis approximatis aut subcontinguis rotundatis, radiis 
medullaribus latis 1-, rarius 2-serialibus e cellulis crassis 1-10, rarius pluribus super- 
positis formatis " {Joe. cit.. p. 30). The figures, cited in the footnote, also agree very well 
with our specimen. On characters of the secondary wood alone, however, one might 
have hesitated in affirming identity, but Mr Kidston's determination has now been 
fully confirmed by comparison with sections of the Falkenberg plant, very kindly lent 
me by Count Solms-Laubach, in one of which the pith and primary wood are included. 
The section in question is shown in an excellent photograph (Plate VII. fig. 10) among 
the illustrations to Count Solms-Laubach's second paper on the Falkenberg Culm- 
fossils^ though on too small a scale for details to be exhibited. The identity of the 

* Araucarioxylon beinertianum, Kr. (Gopp., sp.), 1870-72 ; Araucarioxylon beinertianum, Kraus in Schimper, 
TraitC d. pale'ont. Vegd., vol. ii. p. 381, 1850 ; Araucarites beinertianus, Gopp., Monog. d. foss. Coniferen., p. 233, 
pi. xlii. figs. 1-3 ; pi. xliii. fig. 1, 1852 ; Araucarites beinertianus, Gopp., Foss. Flora d. Uebergangs. Form., p. 254, 
pi. xxxv. figs. 1-4, 1888 ; Araucarites beinertianus, Gopp. u. Stenzel, Nacht z. Kennt. d. Coniferenholzer d..palceoz. Form., 
p. 30, pi. iv. figs. 36-39 ; Araucarites beinertianus, Gopp., Revision d. foss. Gonif., p. 11 (Bot. Centrabl, 1881, vol. v, 
p. 396). 

t " Ueber die in den Kalksteinen des Kulm von Gliitzisch-Falkenberg in Schlesien erhaltenen structurbietenden 
Pflanzenreste. II.," Bot. Zeit., 1893, p. 207. 



PRIMARY STRUCTURE OF CERTAIN PALEOZOIC STEMS. 345 

specimen with the Araucarites beinertianus of Goeppert was established by Count 
Solms-Laubach in conjunction with Stenzel, whom he consulted. 

The preservation is decidedly better than that of the Tweed specimen. The pith 
(about 8 mm. in diameter) contains three sclerotic nests,* and agrees in every respect with 
that of our plant. At three points distinct mesarch strands of primary wood are 
present ; two of these belong to outgoing leaf-traces, while the third, which is smaller, 
has not yet begun to pass out. At several other places small strands of tracheides, 
apparently primary, can be recognised ; most of these were no doubt endarch in their 
development, and they show no clear cases of mesarch arrangement. The secondary 
wood, in both transverse and longitudinal section, shows essentially the same structure 
as in the Tweed specimen, except perhaps that biseriate medullary rays are somewhat 
more frequent. 

Mr Kidston, who has also examined Count Solms-Laubach's sections, agrees with . 
me that they remove all doubt as to the specific identity of the British specimen with 
the Araucarites beinertianus of Goeppert. 

The chief results relating to C. beinertiana are the following : — 

(1) The relatively large pith contains 'sclerotic nests' resembling those in the pith 
of Lyginodendron. 

(2) Around the pith, and in contact with the secondary wood, numerous primary 
xylem-strands, sometimes laterally confluent with one another, are disposed. 

(3) The primary strands attain their largest size where they enter the wood ; at this 
point they resemble the corresponding bundles in C. fascicularis, and are of mesarch 
structure. 

(4) The small strands are more usually endarch, and sometimes of a horse-shoe form, 
the opening being turned towards the pith, and the protoxy]em lying in the concavity 
of the strand. 

(5) A single strand constitutes the leaf-trace, where it enters the secondary wood. 

(6) The secondary wood has a regular Cordaitean structure, with medullary rays 
seldom more than one cell thick. 

(7) A scale-bark was formed on the older stems. 

The reasons for placing this species in the genus Calamopitys are apparent at once 
from the foregoing description. The detailed structure of both primary and secondary 
wood is so closely similar in the two species, that if C. fascicularis is rightly placed in 
Unger's genus, it is impossible to doubt that the other species must accompany it. 
Naturally, both determinations, though resting, as it seems to me, on good grounds, 
must be regarded as provisional until the characters of the cortex and leaf -bases are 
known. In the meantime, it is interesting to note that in the same beds which yielded 
the specimen of C. beinertiana, Mr Kidston found a petiole — provisionally named by 
him Rachiopteris multifascicularis — which presents very much the same structure as 
the small Kalymma-like leaf-bases borne on the stem of Calamopitys Saturni. 

* Solms-Laubach, loc. cit., p. 208. 



346 DR D. H. SCOTT ON THE 

Distinctive specific characters of C. heinertiana are to be found in the large size and 
peculiar structure of the pith, the relatively small extent of the primary xylem, the 
frequent endarch structure of the smaller primary strands, and the usually somewhat 
scattered arrangement of the pits on the secondary tracheides. 

II. Pitys, Witham, emend. 

1. Pitys antiqua, Witham. 

The structure of this stem has been investigated principally in a specimen from Mr 
Kidston's collection (sections 598a-598h), collected by Mr B. N. Peach, F.R.S., at 
Lennel Braes in Berwickshire, in 1883. The specimen, like those already described, 
is of Lower Carboniferous age (Calciferous Sandstone Series). Its specific identity has 
been established by comparison with Witham's type-specimen, as will be explained 
below. 

In this case, also, I am indebted to Mr Kidston for calling my attention to the 
peculiarities of the fossil, and lending me his sections for investigation. 

The stem is remarkable for its large pith, which in the specimen collected by Mr 
Peach, has a diameter of 22 mm. (phot. 5). In a section from another specimen, also 
from Lennel Braes (No. 221 in Mr Kidston's collection) the pith as preserved is as much 
as 34 mm. in diameter, and may be incomplete. The structure of the pith is character- 
istic ; it consists of large, but very short cells, their width, which usually exceeds their 
height, being from '15 to "2 mm. (see figs. 14, 15, and 16). Many of the pith-cells are 
filled with dense carbonaceous contents, suggesting that they may have been secretory 
elements. Although they do not differ in form from the surrounding, comparatively 
empty cells, yet their somewhat regular arrangement, and the fact that their relative 
frequency is unaffected by the state of preservation, may indicate that some real 
differentiation existed during life. 

A conspicuous feature of the pith is the presence of large, horizontal, lenticular gaps 
in its tissue (see phot. 6). These gaps are largest in the outer part of the pith, though 
they are present to some extent all through it. They appear to be due to a shrivelling 
of the tissues, for the cells between the larger gaps are flatter than elsewhere, and 
have a collapsed look. The gaps extend out into the principal medullary rays. 
Their presence gives the pith, as seen in radial section, an appearance not unlike 
that of the well-known discoid pith of Cordaites, but much less regular. It may be 
doubted whether the resemblance is more than a superficial one. The Cordaitean 
discoid structure, as shown, for example, in Cordaites Brandlingi* is strikingly regu- 
lar, and appears to have been due to rupture during a normal process of growth ; the 
gaps are strictly limited to the middle part of the pith, the peripheral zone being un- 
interrupted ; neither do the cells show any signs of collapse. In all these points the 
pith of Pitys antiqua is different ; here the imperfectly discoid structure has much 

* Scott, Studies in Fossil Botany, fig. 137, A ; Eenault, Cours de Bot. Fossile, vol. i. pi. 12, fig. 12. 



PRIMARY STRUCTURE OF CERTAIN PALEOZOIC STEMS. 



347 



more the appearance of having been caused by unequal contraction of the tissue, per- 
haps after death.* Where the specimen is badly preserved, the gaps are much ex- 
aggerated. The pith has evidently undergone dilatation, as shown by the increase in 
width of the medullary rays at their inner ends, and by the marked horizontal elonga- 
tion of many of the pith-cells (PL II. phots. 8 and 9, PL V. figs. 14-16). The latter 
feature is especially conspicuous around the primary xylem-strands, from which the 
dilated medullary cells usually radiate out in all directions (phots. 8 and 9, figs. 14 
and 15). This is a familiar phenomenon wherever lignified strands occur in the midst 
of an actively-growing cellular tissue, as, for example, in fleshy roots. 

The chief point of interest in the stem of Pitys antiqua is the presence of numerous 
strands of primary xylem around the pith, and for the most part embedded in its tissue. 
Their distribution is shown in diagram 5, prepared by Mr L. A. Boodle, in which all 



2 ' *J 




the strands shown in a transverse section have been accurately plotted, in their exact 
position, with the aid of the camera lucida. The total number of xylem-strands present 
in this section was 46. It will be noticed that, with few exceptions, they are separated 
by an appreciable interval from the inner edge of the secondary wood. Actual contact 
is only shown at three points, namely, in the case of the strands numbered 13, 23, 40. 
All the others are separated from the wood by distances ranging from *3 mm. to 1*8 
mm.f The xylem-strands themselves vary in diameter from about *15 mm. to about *3 
mm., so their distance from the wood almost always exceeds their own diameter, and is 
often many times as great. Strands 13 and 40 are double (cf. PL V. fig. 14 for strand 
13) ; we know, from the evidence of successive transverse sections, that strand 13 passed 

* Similar lacunae are present in the central tissue (primary wood) of Megaloxylon. See Seward, " Notes on the 
Binney Collection of Coal-Measure Plants " ; Part ii., Megaloxylon. Proc. Cambridge Phil. Soc, vol. x., 1899. 

t Of course only that part of the section in which the secondary wood is present is taken into consideration. 

TEANS. ROY. SOC. EDIN, VOL. XL. PART II. (NO. 17). 3 f 



348 DR D. H. SCOTT ON THE 

out into the secondary wood a little higher up the stem. The gap shown at l.t. on 
diagram 5 (see also phot. 5), clearly marks the course of another outgoing leaf- trace. 
The strand 23 also seems to be double, but here the tissue is damaged. From the 
somewhat slender evidence available, it seems probable that contact between a primary 
strand and the secondary wood only occurs at points where the former is about to pass 
outwards, presumably on its way to a leaf. It also appears that, at the point of exit 
from the pith, the leaf-trace was a double strand, but its two branches, as we shall see, 
re-united in passing through the wood. Double or paired strands may also occur 
elsewhere, independently of outgoing leaf-traces (see, for example, phot. 8, represent- 
ing strand 38 in diagram 5). The diagram is taken from a section higher up the stem, 
where the two strands have approached nearer to each other. 

Before further considering the distribution of the xylem-strands, it will be well to 
describe their structure. The strands, as already mentioned, are small, indeed very 
small in comparison with the size of the pith. Most commonly their maximum 
diameter is about - 25 mm. ; the sectional form of the strand is usually elliptical, the 
major axis lying in the tangential direction. A good typical example is shown, in 
transverse section, in fig. 15, which represents the strand numbered 3 in diagram 5. 
The smallest elements (px) lie near the middle of the strand ; towards its periphery 
the tracheides become considerably larger, about equalling the innermost elements of 
the secondary wood in size. A few parenchymatous cells occur among the primary 
tracheides, especially near the middle of the group. Phot. 8 shows the same structure 
in each strand of the paired bundle numbered 38. Of the two strands shown in phot. 
9, one (No. 14) shows the usual arrangement of the elements; the other (13a) is less 
regular. Longitudinal sections show the nature of the elements. Fig. 16 is from a 
tangential section (shown as a whole in phot. 7) which passes through the periphery of 
the pith, and here cuts through the middle of a xylem-strand. The more central 
tracheides have an evident spiral thickening ; the narrowest among them are no doubt 
the actual protoxylem. The peripheral tracheides of the strand are larger, and their 
cells definitely reticulated, the lines of reticulation having a spiral course (fig. 16, r. t.). 
Close examination shows that, in the outer tracheides, each mesh is bordered, so that 
the reticulation is passing over into a system of spirally arranged, bordered pits. 
Similar elements, one of which is shown in detail in fig. 1 7, occur at the inner margin 
of the secondary wood, where, however, no true spiral tracheides have been detected.* 

Fig. 16 also shows the xylem-parenchyma, with possible secretory sacs, within the 
primary bundle. 

The evidence thus indicates that the primary xylem-strands of Pitys antiqua have a 
mesarch structure, differentiation having begun at a point near the middle of the strand, 
as indicated by the position of the spiral tracheides. The mesarch structure holds good 

* I fiiid that perfectly similar elements have been described by Rothert, in recent Conifers, under the name of 
" Gemiscbte Gefasse." See his " Tracheiden u. Harzgange im Mark von Cephalotaxus-Arten," Ber. d. Detttsch. Bot. 
Gesellsch., Bd. 17, 1899, p. 284. 



PRIMARY STRUCTURE OF CERTAIN PALAEOZOIC STEMS. 349 

for the great majority of the strands ; in a few of the smallest the protoxylem may lie 
on one side or the other (e.g., the strand 13a shown in phot. 9). 

At the point where a double bundle comes into contact with the secondary wood 
previous to passing out into the latter, the structure is less regular. Fig. 14 shows 
this in the case of the double strand numbered 13. The smallest elements of the two 
xylem-strands are here directed towards each other, and some of them abut directly on 
a wedge of secondary wood. In a section cut a little further up the stem, where this 
bundle is shown entering the wood on its outward course, it appears as a single strand, 
the two half-bundles having re-united. It is possible that their temporary separation 
may have been due merely to the intrusion of dilated parenchyma. 

The similar outgoing strand between bundles 5 and 6 (l.t. in diagram 5 and phot. 
5), though obscure, and difficult to distinguish from the adjacent secondary wood, is 
clearly a single one. It is remarkable how small were the dimensions of the leaf-trace 
(as we must assume it to have been), at least as regards its primary xylem. Possibly it 
was supplemented on its outward course by an arc of secondary wood, as was the .case 
in Poroxylon, * but at present we have no information as to any of the external 
tissues of our fossil. It will be noticed that behind each of the outgoing strands 1 3 and 
40 (diagram 5) there is a small xylem-bundle deeply embedded in the pith (12a and 
39a respectively) ; the strand 5 stands in a similar relation to the leaf-trace, l.t. The 
strand 12a is shown in detail in fig. 14. In this case there is a second deep-seated 
strand near by (13a, shown in phot. 9). In the uppermost of the five successive trans- 
verse sections of the stem which we possess, where the strand 13 is beginning to enter 
the wood, the two deep-seated strands, 12a and 13a, are approaching each other as if 
about to fuse, but there is no evidence to show whether such a fusion was of general 
occurrence. In any case it is natural to regard the deep-seated strand behind the leaf- 
trace as a reparatory strand, destined to constitute or contribute to the next outgoing 
bundle of the same orthostichy. 

The phyllotaxis was no doubt a spiral one, and very probably complex, as suggested 
by the large number of primary strands. 

There is evidence that the primary strands occasionally branched and anastomosed 
with one another. This is best seen in a tangential section, passing through the outer 
part of the pith, and touching in places on the secondary wood, represented in phot. 7. 
Several of the primary xylem-strands are shown ; the double strand, which corresponds 
almost exactly in size and position with some of those shown in transverse section (cf. 
fig. 14), is in contact with the innermost tracheides of the secondary wood, and may 
probably represent a leaf-trace about to pass out. An oblique anastomosis between the 
strands of this pair is present. 

Another strand appears to be branching, and at several places single tracheides are 
seen diverging from the xylem-strands in various directions, probably to form a 
connection with others. 

* Cf. Pitys Withami, below, p. 355. 



350 DR D. H. SCOTT ON THE 

Such isolated tracheides, either between two xylem-strands, or between a xylem- 
strand and the secondary wood, are not infrequently met with in the transverse 
sections, as shown in phot. 9, between the strands numbered 14 and 13a in diagram 
5. It is probable that these elements served to keep up communication between 
different strands, though in some cases their separation from the bundle to which 
they belonged may have been an accidental effort of the dilatation of the adjacent 
parenchyma. 

The wide separation between most of the primary xylem-strands and the secondary 
wood presents a considerable difficulty, which exists also, though in a less degree, in the 
case of Calamopitys fascicularis, and probably other species of that genus. In Pitys 
antiqua, as mentioned above, the actual distance ranges from about a third of a 
millimetre to almost two millimetres. The average interval, it is true, is only about half 
a millimetre, but this is equal to twice the average diameter of the xylem-strand itself. 
Cases of contact are rare, and probably limited to bundles approaching their exit. 
Apart from these special cases, we find that the number of pith-cells intervening 
between a primary strand and the wood varies from one up to about twenty, averaging 
five or six. 

The question arises : What could have been the primary structure of a stem in which 
such an arrangement prevailed ? If, as all the evidence indicates, the process of 
secondary growth was of the normal type, the secondary wood being intercalated 
between the primary xylem and the phloem, it follows that in the primary condition 
the xylem and phloem of each bundle must have been widely separated, and that to a 
very unequal extent in different bundles, unless indeed the isolation of the xylem- 
strands can be explained by subsequent dilatation of the parenchyma. We have 
already seen that this took place to a considerable extent ; in some cases the apparent 
doubling of a xylem-strand has evidently been brought about by tangential dilatation of 
its own fascicular parenchyma, and the isolation of single tracheides may sometimes 
have been due to a similar cause. But I have found no evidence that in Pitys antiqua 
the dilatation was greater between the xylem-strand and the secondary wood than else- 
where. It rather appears that the relative position of the two has remained approxi- 
mately constant, though the absolute distance between them has no doubt been 
increased by the general extension of the parenchyma. If this were so, there must 
have been from the first an unusual separation, varying in different bundles, between 
xylem and phloem, and the cambium must have arisen towards the phloem-side of the 
intervening tissue, thus leaving the primary xylem more or less isolated. The tissue 
between primary and secondary wood would, on this view, have originally been fascicular, 
but have become assimilated to the pith by subsequent dilatation. The position of the 
specially deep-seated xylem-strands, behind the outgoing leaf-traces, remains a difficulty, 
and I do not think that the whole question will be solved until young stems are 
discovered. Some analogy for the separation of primary from secondary wood is 
afforded by the peduncles of certain Cycads (especially Stangeria) where the centripetal 



PRIMARY STRUCTURE OF CERTAIN PALAEOZOIC STEMS. 351 

is often rather remote from the centrifugal wood.* A similar separation is of common 
occurrence in roots, especially those of Gymnosperms. 

Two other explanations are theoretically possible, though I believe really untenable. 
We might suppose that the cambium was extrafascicular, the xylem-strands thus 
representing complete vascular bundles. I have not, however, found the least indi- 
cation of phloem in connection with them, and the preservation is sufficiently good to 
leave little doubt that none existed, and that the xylem-strands were surrounded on all 
sides by parenchyma only. 

The other possibility is that the xylem-strands may not have constituted the 
primary xylem of the leaf-trace system, but may have formed a merely accessory 
system of medullary strands, remotely comparable to the medullary bundles of 
Encephalartos, Macrozamia, or even, as some might suggest, to the star-rings of 
Medullosese. The absence of phloem is an obvious objection to this view also, and 
even apart from this, the facts that the xylem-strands pass out through the secondary 
wood, and that they are the only part of the wood where spiral elements occur, seem 
fairly decisive for their primary nature, as part of the main leaf-trace system of the 
plant. The very remarkable medullary xylem found by Eothert in a Conifer, which 
he refers to Cephalotaxus Koraiana, offers a certain analogy with that of our fossil, 
but, in the case of this recent plant, no spiral elements occur among the medullary 
tracheides.t 

The general structure of the secondary wood of Pitys antiqua has long been 
known,! but as Mr Kidston's specimen (No. 598) is probably the best-preserved of any 
hitherto investigated, a short description may be given, more especially as the existing 
accounts are inaccurate in various points. 

The chief generic character of Pitys, as at present defined — the wide medullary 
rays — is well exhibited. The principal rays are usually much wider at their inner ends 
than elsewhere. A ray '3 mm. in tangential width at its junction with the pith may 
diminish to a tenth of that width in a distance of little more than a millimetre (fig. 
14, phot. 8). The difference depends more on the width of the individual ray-cells 
than on their number, which remains nearly constant, and is evidently due, in great 
part, to dilatation occurring during the early stages of wood-formation. The gaps in 
the pith, referred to above (p. 346), run out for some distance into the principal 
medullary rays. Close to the pith, where the rays are wide, the nature of these gaps, 
as mere tears in the tissue, is evident ; further out, as the rays become narrower, the 
gaps assume a more regular form, and sometimes strongly suggest the resin-canals in 
the rays of Abietineae (see PI. VI. fig. 20, g). This appearance is in all probability 

* Scott, " Anatomical Characters presented by the Peduncle of Cycadaceee," PI. XX. figs. 1-5, Ann. Bot, vol. xi., 1897. 

t Rothert, I.e. It is interesting to find (p. 285), that Rothert's "gemischte Gefasse" occur in the medullary as 
well as in the normal wood of his Cephalotaxus, just as is the case in Pitys antiqua. 

% Witham of Lartington, Internal Structure of Fossil Vegetables, Edinburgh, 1833, pp. 25-27, 37, 38, 71, pi. iii. ; 
pi. iv., figs. 1-7 ; pi. vii., figs. 9-12 ; pi. viii., figs. 1-3 ; pi. xvi., figs. 9, 10. Little appears to have been added 
by later writers. 



352 DR D. E SCOTT ON THE 

deceptive, and the spaces due simply to the contraction of the surrounding tissue. 
Traced out into the wood, the rays soon assume the ordinary structure ; their tissue, 
as seen in radial section, has the usual muriform character (see PL V. fig. 18). The 
cells usually retain some remains of their contents, often in the form of definite granules. 
Secondary rays appear between the principal ones, as best shown in specimens where 
the wood attains some considerable thickness. 

Seen in tangential section (PL VI. fig. 19) the larger rays are found usually to reach a 
width of four cells, sometimes five or even six, and are often of great height, seventy cells 
or upwards in some cases. Among the large rays, however, much smaller ones occur, 
only one cell thick, and of small height, sometimes reduced to a single cell. At one 
or two places an isolated strand of xylem-parenchyma was observed, consisting of a 
row of vertically elongated cells, at least three times as high as those of the rays. 
This tissue is, however, extremely scanty, and in most sections is not shown. 

The tracheides are exquisitely preserved. Those at the inner edge of the secondary 
wood are transitional between the reticulated and pitted forms ; the spirally arranged 
reticulations are distinctly bordered (fig. 17). Further out in the wood, the spiral 
arrangement becomes less marked, and the pits assume the characteristic hexagonal 
form (fig. 18). They are ranged in four or five ranks, on the radial walls of the large 
tracheides, and are usually in contact with one another throughout. Occasionally, how- 
ever, especially near the ends of the tracheides, the pits are more scattered, as Witham 
described them,* and may be even reduced to a single row, leaving the rest of the 
wall bare. The border of each pit is, as a rule, perfectly preserved, enclosing a narrow 
slit or pore, usually in an inclined position (fig. 18). A more perfect example of 
typical ' Araucarioxylon 7 structure than that presented by this wood could not be 
imagined. 

The tangential walls of the tracheides are, as a rule, without pits, but exceptions 
occur, especially in the inner layers of the wood. A good example is shown in fig. 20, 
where a number of pits (t.p.) are seen on the tangential wall of a tracheide. Where 
they occur, they are less crowded than those on the radial walls, and do not cover the 
whole surface. Tangential pits are of common occurrence in the wood of the Coniferse, 
especially in the first-formed layers, and in the tracheides of the autumn wood.f 

We may sum up the chief anatomical characters presented by the stem of Pitys 
antiqua as follows : — 

(1) The pith is large (22 mm. to 34 mm. or more in the specimens examined) and 
consists of short-celled parenchyma, interrupted by extensive horizontal lacunae, prob- 
ably due to shrinkage of tissue. 

(2) Around the periphery of the pith, and usually at some little distance from the 
inner edge of the secondary wood, are a large number (40-50) of small primary xylem- 
strands, which occasionally anastomose with one another. The central elements of each 
strand are spiral tracheides, indicating a mesarch structure. 

* L.c, p. 38. t L.c, Strasburgkr, " Leitungsbahnen," Histologische Beitrage, iii. p. 9, 1891. 



PRIMARY STRUCTURE OF CERTAIN PALEOZOIC STEMS. 353 

(3) At certain points the primary xylem-strands come into contact with the 
secondary wood, and pass out through it ; these outgoing strands no doubt represent 
the leaf-traces. 

(4) The secondary wood is traversed by numerous medullary rays, the larger of 
which are usually four cells or more thick. The principal rays are much dilated towards 
their junction with the pith. In addition to the rays, vertical strands of xylem- 
parenchyma occur, but very sparingly. 

(5) The secondary tracheides have, on their radial walls, several rows of bordered 
pits, usually contiguous and hexagonal. Tangential pits also occur not infrequently. 
No true spiral elements are present at the inner edge of the secondary wood. 

The identification of Mr Kidston's specimen, No. 598, on which the description 
above is based, with the Pitys antiqua of Witham, rests on a comparison with sections 
of Witham's type-specimen, kindly lent me by Prof. Bayley Balfour, F.R.S., and Mr 
Kidston. The specimen from which these sections were cut is the large stem shown in 
transverse section, reduced to half natural size, in Witham's Internal Structure, Plate 
III. The two sections sent me from Edinburgh are originals of Witham's, while those 
lent by Mr Kidston (Nos. 217-220 in his Collection) are better and more modern 
preparations from the same specimen. In all these only the secondary wood is shown. 
The preservation is not equal to that of the stem (No. 598) collected by Mr Peach, but, 
allowing for this difference, the structure essentially agrees. The locality, Lennel Braes 
on the Tweed, is the same. The medullary rays in Witham's specimen are more 
scattered, and sometimes broader than in No. 598, attaining an extreme width of seven 
cells, as against five, or rarely six, in the latter, but these differences may well be due to 
the much greater size of the Witham stem. The dimensions of the elements agree very 
nearly. Where the pitting is well shown in radial section, the arrangement corresponds 
with that in No. 598. At many places the pits are in 3-5 rows, covering the whole 
wall of the tracheide, closely packed and hexagonal in outline, quite like those shown 
in fig. 18, except that, as the preservation is not so good, the outline of the borders is 
less sharp. In other places the pits are more scattered and rounded in outline, as also 
occurs in the other specimen. There is a section in Mr Kidston's collection (No. 221) 
which, he tells me, may be from a different specimen. This is the section referred to 
above (p. 346) as showing a pith at least 34 mm. in diameter. The state of preservation 
is similar to that of the type-specimen, with which its secondary wood exactly agrees. 
The pith is lacunar, and primary strands of xylem are present, just as in No. 598. A 
transverse section of a branch, figured by Witham (PI. VII., fig. 11), with a pith more 
than 3 cm. in diameter, has quite the anatomical habit of our fossil (cf. phot. 5). 

Considering the identical locality, I feel no doubt that the specimen on which the 
description given in the preceding pages is based, is referable to Witham's species, 
Pitys antiqua, his 'Lennel Braes Tree.' 



354 DR D. H. SCOTT ON THE 

2. Pitijs Withami (Lindl. et Hutt., sp.). 

I take this species to include the P. medullaris of Lindley and Hutton, which 
Witham himself regarded as probably identical with the former.* There seems no 
object in keeping up the two specific names, as the characters on which P. medullaris 
was separated — the large pith, and the appearance of concentric markings (probably not 
annual rings) in the wood, are common to many stems of the Dadoxylon group, and of 
no diagnostic value. Both were included in the old genus Pinites of Lindley and 
Hutton, which, as employed by those authors, has long since been abandoned. The 
distinction drawn by Witham t between Pinites and Pitys, and based on the round, 
separate pits in the case of Pitys, and the hexagonal contiguous pits in that of Pinites, 
has no value, as both conditions are found, in different parts of the same specimen. 
Pitys Withami is, in fact, a closely-allied species to P. antiqua. The pitting on the 
tracheides is identical (if equally well-preserved specimens are compared), and there is no 
constant difference in the size of the elements. The medullary rays are, however, on the 
whole narrower in P. Withami than in P. antiqua, rarely exceeding four cells in width in 
the former. The point of interest for our present purpose is that Pitys Withami shows 
the same primary anatomical structure as P. antiqua, having, like that species, a ring 
of primary xylem-strands disposed round the pith. My observations were made on an 
original section of Witham's (figured in Internal Structure, PI. VI., figs. 5-8), lent me 
by Professor Bayley Balfour. This section was from the branch to which Lindley and 
Hutton gave the name of P. medullaris ; it is represented as a whole in PL II. phot. 10. 
The pith, which measures 19 x 10 mm., shows essentially the same structure (so far as 
exhibited in transverse section) as that of P. antiqua, but much of the tissue is altered in 
appearance by the infiltration of some dark-brown substance. The preservation is 
tolerably good, but towards the wood, where the cells become smaller, the structure is 
obscure, partly owing to the section not being sufficiently thin. Yet at several places 
small strands of thick-walled elements can be distinguished lying near the outer margin 
of the pith, a little within the ring of secondary wood. These groups agree so closely, 
in appearance and position, with the primary xylem-strands of P. antiqua, that we can- 
not doubt their identical nature. The strand figured (PL VI. fig. 21) appears to be a 
double one. 

The secondary wood is described by Witham (I.e., p. 32) as showing " decided indi- 
cations of five concentric layers." The layers are marked by tangential bands of some- 
what flattened elements (see Witham, PL VI., fig. 8)4 and the bands, so far as the 
section extends, are fairly, though not completely, continuous. There is thus a certain 
resemblance to the annual rings of recent Coniferse, but very much less marked and 
regular in the fossil, so that (considering the inconstancy of such markings in Palaeozoic 

* Internal Structure, pp. 36 and 42. Pitys Withami was founded on the well-known Craigleith trees discovered 
in 1826 and 1831 in the Craigleith Quarry, near Edinburgh. 

t Who, however, himself had some doubts as to the generic value of the distinction. L.c, p. 39. 

\ This figure gives a fair idea of the relative forms of the elements, but the dark shading makes the rings appear 
more conspicuous than they really are. 



PRIMARY STRUCTURE OF CERTAIN PALEOZOIC STEMS. 355 

stems) it would be extremely rash to draw any inference as to a seasonal periodicity of 
growth. 

At one place a bundle, no doubt a leaf- trace, is clearly shown, passing out 
through the wood (see phot. 10, l.t.). A very definite arc of secondary wood forms 
part of the outgoing leaf-trace, and is sharply marked off from the general wood of the 
stem. This observation confirms the conclusion, drawn from Pitys antiqua, that in this 
genus the leaf-traces, on leaving the pith, were single strands. 

So far as the evidence extends, there was thus a complete agreement in the primary 
structure of the stem between Pitys Withami and P. antiqua. 

3. Pitys primseva, Witham. # 

This species, one of Witham's Tweed Mill fossils.t is a very distinct form, as shown 
by the great width of the medullary rays, which are commonly seven cells in thickness 
and often more, and of a decidedly broader and shorter form, in tangential section, than 
those of P. antiqua or P. Withami (see fig. 22). The tracheides, also, are larger, and 
the pitting slightly different, the pits of P. primseva being less crowded than those 
of the other species. Hence the hexagonal form is less marked and a circular outline 
more frequent in the pits of P. primseva than in those of its congeners. 

As regards the question of primary xylem-strands, the material at my disposal was 
not favourable, as I have seen no sections passing through the pith of a main stem. 
In one case, however, a tangential section happens to cut transversely across the base of a 
lateral branch (PI. II. phot. 11). The pith of the branch is only partly preserved ; what 
remains of it resembles that of P. antiqua. At two places in the pith, near the wood, 
I observed a group of small, rather thick-walled elements, similar to the tracheides of 
the secondary xylem. At one point the spiral band of a tracheide could be recognised. 
The pith-cells are elongated radially around the groups in question, and the whole 
appearance (allowing for the imperfect preservation) is in all respects similar to that of 
the primary xylem-strands in P. antiqua. 

The same tangential section is also of interest from another point of view, for it 
appears to throw light on the problematic fossil described by Williamson under the 
name of Lyginodendron (?) anomalum.% In the section of P. primseva (phot. 11), 
the medullary rays near the lateral branch have a form very different from that which 
characterises them elsewhere (see fig. 23, and compare with fig. 22). They are shorter 
than usual, and at the same time much wider, so as sometimes to assume a nearly 
circular form, as seen in the tangential section. These exaggerated medullary rays 
constitute in this region the great mass of the wood, the strands of tracheides merely 
forming a sinuous network between them. The appearance is almost identical with 

* Sections of two specimens, one from the River Irthing, Northumberland, the other from Juniper Green, Mid- 
lothian, were lent me by Mr Kidston for investigation. Both are from the Calciferous Sandstones. 
t L.c, pp. 38, 71, pi. viii., figs. 4-6. 

X " Organization of Fossil Plants of Coal-Measures," Part IX., Phil. Trans., 1878, pt. ii. p. 352, pi. 25, figs. 90-92. 
TRANS. ROY. SOC. EDIN., VOL. XL. PART II. (NO. 17). 3 g 



356 DR D. H. SCOTT ON THE 

that presented by the tangential section of Lyginodendron anomalum (Williamson, 
loc. cit., fig. 92), except that in the latter the dilated medullary rays are on a still larger 
scale. 

In Pitys primseva the dilated rays are limited to the neighbourhood of the lateral 
branch, becoming normal at a greater distance from it. 

The puzzling structure of Lyginodendron anomalum, which is only known as a 
fragment of calcified wood from the volcanic ash of Arran, was correctly interpreted by 
Williamson, who says (I.e., p. 352) : " These cell-masses are in fact huge medullary 
rays of a most extraordinary form." No stem, however, has hitherto been known, 
presenting the same peculiarity in so extreme a degree. Mr Seward, who observed a 
somewhat similar enlargement of the rays near the outgoing leaf-trace, in the stem 
named by him Lyginodendron robustum, made the following suggestion : " Such a 
comparison suggests the probability that the shorter and broader medullary rays and 
the more irregular course of the tracheides may not represent the normal character of 
the stem from which the Arran fragment was obtained, but that these appearances may 
be the result of some disturbing influence in the secondary wood." * In the specimen 
of Pitys primseva just described, we have a striking confirmation of Mr Seward's 
suggestion. Under the ' disturbing influence ' of the presence of a lateral branch, the 
wood of this plant assumes the same peculiar structure which characterises the Arran 
fragment, while elsewhere retaining the ordinary organisation. 

In other respects, and notably in the pitting of the tracheides, there is a close, 
though not an absolutely exact agreement between the wood of Pitys primseva and 
that of the Arran fossil, which is of similar Lower Carboniferous age. It is possible 
that the two are specifically identical, the specimen known as Lyginodendron anomalum 
being simply a fragment of a large stem of Pitys primseva, from a part affected by the 
presence of some bulky appendage. Until further evidence is obtained, it may be well 
to keep up Williamson's specific name, but the genus is presumably Pitys rather than 
Lyginodendron. 

The Genus Pitys. 

Apart from the doubtful fragment last mentioned, all the species of Pitys, as limited 
by GoEPPERT,t pr